Research Interests

Statistical theory (estimators – asymptotic properties)

Statistical applications (medical statistics, econometrics)

Degrees

PhD in  Mathematics,  University of Zagreb , 1997.

MSc in Mathematics,  University of Zagreb ,1990.

BSc in Mathematics and Physics, University of Osijek, Croatia, 1985.

Publications

1. Š. Dario, M. Benšić, D. Šubarić, D. Paulik, V. Barišić, Đ. Ačkar, Influence of High-Voltage Electrical Discharge on the Oil Binding Capacity of Spelt Chaff and Whey, Hrana u zdravlju i bolesti 15/1 (2026), 10-16
2. A. Liović, Z. Kolundžić, K. Pavičić Dokoza, M. Benšić, Đ. Ačkar, The Hidden Cost of Teaching: An Integrative Model of Vocal Demand, Vocal Fatigue, and Voice Handicap in Teachers, Journal of voice (2026), 1-9
3. P. Vukotić, V. Radolić, R. Svrkota, D. Stanić, T. Anđelić, M. Benšić, R. Mrdak, B. Fuštić, Comparison of radon in karst area and area with clastic bedrock in Montenegro, The European physical journal. Special topics 1/ (2026), 1-11
4. P. Vukotić, M. Benšić, V. Radolić, Distribution of radon concentrations on the ground floor of schools and kindergartens, Applied Radiation and Isotopes 236/112760 (2026), 1-8
5. E. Kovač-Andrić, M. Benšić, V. Gvozdić, M. Jozanović, N. Sakač, A. de Souza, Identifying Significant Meteorological Predictors for the Monthly Number of Hotspots in Brazilian Biomes, Sustainability 18/3363 (2026), 2-20
   Abstract

   Forest fires release various chemical compounds that directly degrade air quality and endanger human health. This study examines the occurrence of forest fires in six Brazilian biomes over a 22-year period (1999–2021). The primary purpose is to identify significant meteorological predictors for the monthly number of hot spots using a standardized statistical framework. Fire hotspots were identified using satellite thermal sensors (AVHRR and MODIS), and we employed a standardized negative binomial regression modeling approach to analyze the relationship between meteorological variables and fire hotspots in all six Brazilian biomes simultaneously, providing a comprehensive comparative perspective often lacking in studies focused on isolated regions. The results show that the Amazon and Cerrado biomes have the highest absolute number of fires, which is consistent with their size and vegetation structure. To avoid bias associated with biome size, fire occurrence was additionally estimated using hotspot density normalized by biome area (hotspots per km2). Using these models, significant factors for fire occurrence were identified, namely the main meteorological variables—temperature, precipitation and wind speed. By comparing the performance of the models in different biomes, we aimed to better understand regional fire dynamics. The model’s ability to predict the expected number of fires based on these variables provides a key tool for preventive air quality monitoring. Such a predictive model serves as a basis for developing early warning systems, assessing potential health risks for the population, and adopting targeted fire management policies.
6. Đ. Ačkar, Š. Dario, V. Barišić, M. Benšić, M. Smiljanić, D. Paulik, Influence of high-voltage electrical discharge treatment on oil binding capacity of fava bean protein and cocoa shell, Food Science and Technology 20/1 (2026), 93-100
7. N. Šarlija, M. Benšić, THE DOUBLE-EDGED SWORD OF SALES GROWTH: IMPLICATIONS FOR SMES INSOLVENCY RISK, The South East European Journal of Economics and Business 21/1 (2026), 15-29
   Abstract

   Research on SME insolvency is one of the most important areas in economy because it is crucial for economic growth which would not be possible without growing firms. These two phenomena - insolvency and growth are typically studied independently. This study brings them together by examining the interaction between sales growth and insolvency among small and medium enterprises (SMEs). On the dataset of financial ratios for Croatian SMEs by applying logistic regression with interaction effects, it is investigated how sales growth, leverage and liquidity affect the probability of insolvency. The results showed that sales growth decreases the risk of insolvency, but that it depends on the level of indebtedness of SMEs. The least risky are those SMEs whose sales growth is supported by an adequate level of capital. SMEs with high sales decline have the highest probability of insolvency even when leverage and liquidity are suitable.
8. I. Mihin Huskić, M. Benšić, K. Kretonić, I. Miškulin, M. Miškulin, J. Milas, D. Nujić, Duration of protection from severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) after primary homologous vaccination or first infection, Vaccine 62/127440 (2025)
   Abstract

   The aim of this study was to determine the duration of protection in 95 % of the population after primary vaccination (PV) and/or acquiring SARS-CoV-2 infection in order to make public health decisions. A study was a retrospective cohort study conducted in Osijek-Baranja County, Croatia, between December 27, 2020, and May 12, 2023. A total of 119,596 subjects of both sexes and all age groups were analyzed. The method of survival analysis was used. The length of protection (LoP) for 95 % and 90 % of the population with first infection was 256 (confidence interval (CI) 251–264) days and 365 (CI 350–381) days, respectively. In those primarily vaccinated, the longest duration of protection was recorded in subjects having received primary homologous vaccination with Spikevax (Moderna), 143 (CI 133–150) and 192 (CI 183–201) days, followed by those with Comirnaty (BioNTech/Pfizer), 119 (CI 116–122) and 168 (CI 165–170) days, respectively. The respective duration of protection was 77 (71–84) and 164 (154–172) days for Jcovden (Janssen-Cilag), and 125 (118–131) and 149 (144–154) days for Vaxzevria (AstraZeneca). Protection after SARS-CoV-2 infection was longest as compared with the LoP following primary vaccination with any of the vaccines. The interval for vaccination of the general population previously infected with SARS-CoV-2 is on average twice the protection provided by primary vaccination with any homologous vaccine. Conclusions based on the study results are relevant for making public health measures concerning re-vaccination timing.
9. P. Vukotić, V. Radolić, R. Svrkota, D. Stanić, T. Anđelić, R. Mrdak, B. Fuštić, M. Benšić, RADON in a high karst area of Montenegro – A case study, Applied Radiation and Isotopes 217/111669 (2025), 1-8
   Abstract

   The national radon surveys in Montenegro revealed that the highest annual average radon concentrations (CRn,ind) in ground floors of dwellings and schools were found in a rural region characterized as a typical high-karst area. In this region, spanning approximately 800 km2, CRn,ind values in 9 houses and 16 schools ranged from 219 to 2494 Bq/m3, with AM = 977 Bq/m3. To investigate the causes of these elevated indoor radon concentrations, the following parameters were measured near the 25 surveyed buildings: soil humidity, electrical conductivity, pH, activity concentrations of 226Ra, 238U, 235U, 232Th and 40K, radon concentration in soil gas (c), soil permeability for radon gas (k), and gamma dose rate in the air. The geogenic radon potential (GRP) of the location was calculated based on the measured values of c and k. As anticipated, the soil permeability in this karstic region was notably high, 1.53·10−11 m2 on average, resulting in elevated GRPs and radon indexes (RI). Therefore, 9 investigated locations were classified as having an Extremely High RI, and the other 9 as having Very High RI. Building characteristics, such as filling, wall material, floor slab quality (FSQ), window frames, and construction period, were also assessed. A multivariate regression analysis was performed to evaluate the relationship between CRn,ind and independent variables of geogenic origin, as well as those related to building construction. The optimal linear regression model, with predictor variables FSQ, c, k, GRP and 238U, can explain 29.1% of the variance of indoor radon concentrations.
10. V. Barišić, Đ. Ačkar, I. Lončarević, J. Petrović, M. Benšić, D. Paulik, K. Doko, A. Jozinović, J. Babić, D. Šubarić, Cocoa Shell as a Bulking Agent in Nutritionally Improved Cocoa Spreads with Sugar Substitutes , Current research in nutrition and food science 12/3 (2024)

11. N. Karakaš Janjić, T. Kalman Šipoš, V. Prelog, M. Benšić, Determination of the mechanical properties of recycled brick aggregate concrete by multivariate regression analysis, Advances in Civil and Architectural Engineering 15/29 (2024), 151-167
    Abstract

    This study presents regression models for prediction of compressive strength and modulus of elasticity, applying variables such as the percentage of recycled brick aggregate replacement, cement content, and water-cement ratio. A comprehensive database was constructed, comprising data from 180 experimental tests conducted on recycled brick aggregate concrete. The database includes the findings of compressive strength and modulus of elasticity testing. Multivariate statistical analysis was performed on the data and prediction models were created. During the review of the existing literature, a research gap was observed, where the modulus of elasticity was always expressed with dependence on compressive strength. The modulus of elasticity and compressive strength are modelled separately using the values of the contents of the concrete mixture. From the derived equations, the relationship that the modulus of elasticity is the second root of the compressive strength is recognized, which is in accordance with the functional relationships of the modulus of elasticity and compressive strength determined by previous authors. These models were then evaluated and confirmed using a subset of 20 samples for compressive strength and 13 samples for modulus of elasticity, which were excluded from the main database. The main results confirmed the applicability of the proposed equations with acceptable accuracy for initial concrete mixtures and thus, can be used as guidelines by future researchers.
12. A. Jozinović, J. Panak Balentić, Đ. Ačkar, M. Benšić, J. Babić, V. Barišić, A. Lončarić, B. Miličević, D. Šubarić, Nutritionally Valuable Components and Heat-Induced Contaminants in Extruded Snack Products Enriched with Defatted Press Cakes, Molecules 29/4 (2024), 791-804
    Abstract

    This research studies the influence of the addition of defatted press cakes (from the production of hazelnut, camelina, pumpkin, and hemp seed oil) on nutritionally important components: fibre, resistant starch, polyphenols, hydroxymethylfurfural (HMF), and acrylamide in directly and indirectly expanded snacks. The amounts of press cakes added to corn grits were 3, 6, and 9%. Extrusion was carried out in a laboratory single-screw extruder. For indirectly expanded products (SCFX), supercritical CO2 was injected during extrusion, and secondary expansion was completed in the microwave oven. The type and content of press cake, as well as the type of product, significantly influenced total polyphenol content and antioxidant activity. Press cakes increased the contents of both soluble and insoluble fibre (from 1.94% d. m. and 1.28% d. m. for extrudates without press cakes up to 3.17% d. m. and 6.94% d. m. for SCFX extrudates with press cakes, respectively), and resistant starch was not markedly influenced by their addition. The influence of the content of press cake on HMF was not significant, whereas the type of cake and the type of extrusion influenced HMF significantly. In a raw mixture of corn grits with 3% of pumpkin press cake, HMF was below the limit of detection, and the highest content was found in the classically extruded sample with the addition of 9% of camelina press cake (580 ppb). In all samples, the acrylamide content was below the limit of detection, indicating that safe products were obtained. This research shows potential for the implementation of supercritical CO2 extrusion in the production of safe, nutritionally improved snack products. Future research might bring about the design of cost-effective processes applicable in the industry.
13. M. Zvonarić, M. Benšić, I. Barišić, T. Dokšanović, Prediction Models for Mechanical Properties of Cement-Bound Aggregate with Waste Rubber, Applied Sciences 14/1 (2024), 470-485
    Abstract

    The high stiffness of cement-bound aggregate (CBA) is recognized as its main drawback. The stiffness is described by the modulus of elasticity, which is difficult to determine precisely in CBA. Incorporating rubber in these mixtures reduces their stiffness, but mathematical models of the influence of rubber on the mechanical characteristics have not previously been defined. The scope of this research was to define a prediction model for the compressive strength (fc), dynamic modulus of elasticity (Edyn) and static modulus of elasticity (Est) based on the measured ultrasonic pulse velocity as a non-destructive test method. The difference between these two modules is based on the measurement method. Within this research, the cement and waste rubber content were varied, and the mechanical properties were determined for three curing periods. The Edyn was measured using the ultrasonic pulse velocity (UPV), while the Est was determined using three-dimensional digital image correlation (3D DIC). The influence of the amount of cement and rubber and the curing period on the UPV was determined. The development of prediction models for estimating the fc and Est of CBA modified with waste rubber based on the non-destructive test results is highlighted as the most significant contribution of this work. The curing period was statistically significant for the prediction of the Est, which points to the development of CBA elastic properties through different stages during the cement-hydration process. By contrast, the curing period was not statistically significant when estimating the fc, resulting in a simplified, practical and usable prediction model.
14. M. Ostojčić, M. Cikoja, I. Flanjak, B. Bilić Rajs, T. Moslavac, M. Benšić, M. Brekalo, I. Strelec, S. Budžaki, The Influence of Qualitative Parameters of Waste Cooking Oils and Fat on Fatty Acid Methyl Esters Yield , Kemija u industriji: časopis kemičara i tehnologa Hrvatske 73/11-12 (2024), 439-447
15. S. Guljaš, M. Benšić, Z. Krivdić Dupan, O. Pavlović, V. Krajina, D. Pavoković, P. Šmit Takač, M. Hranić, T. Salha, Dynamic Contrast Enhanced Study in Multiparametric Examination of the Prostate—Can We Make Better Use of It?, Tomography 8/3 (2022), 1509-1521
    Abstract

    We sought to investigate whether quantitative parameters from a dynamic contrast-enhanced study can be used to differentiate cancer from normal tissue and to determine a cut-off value of specific parameters that can predict malignancy more accurately, compared to the obturator internus muscle as a reference tissue. This retrospective study included 56 patients with biopsy proven prostate cancer (PCa) after multiparametric magnetic resonance imaging (mpMRI), with a total of 70 lesions; 39 were located in the peripheral zone, and 31 in the transition zone. The quantitative parameters for all patients were calculated in the detected lesion, morphologically normal prostate tissue and the obturator internus muscle. Increase in the Ktrans value was determined in lesion-to-muscle ratio by 3.974368, which is a cut-off value to differentiate between prostate cancer and normal prostate tissue, with specificity of 72.86% and sensitivity of 91.43%. We introduced a model to detect prostate cancer that combines Ktrans lesion-to-muscle ratio value and iAUC lesion-to-muscle ratio value, which is of higher accuracy compared to individual variables. Based on this model, we identified the optimal cut-off value with 100% sensitivity and 64.28% specificity. The use of quantitative DCE pharmacokinetic parameters compared to the obturator internus muscle as reference tissue leads to higher diagnostic accuracy for prostate cancer detection.
16. I. Netinger-Grubeša, M. Benšić, M. Vračević, New methods for assessing brick resistance to freeze-thaw cycles, Materiales De Construcción 71/e258 (2021)
    Abstract

    The aim of this research is to analyse the reliability of the existing methods, and find new ones, for assessing brick resistance to freeze-thaw cycles. A series of bricks were tested against a range of properties; compressive strength ratios pre- to post-freezing and Maage’s factor, were calculated. Using a database created in this way, an analysis of existing classifiers was carried out and new ones were established based on which bricks could be classified into resistant and non-resistant to freeze-thaw cycles. The median pore radius, the ratio of compressive strengths pre- to post-freezing and the water desorption coefficient at 180-360 minutes proved to be good classifiers with a clearly specified cut-off for the distinction between resistant and non-resistant bricks with an acceptable risk of a wrong decision. The ratio of compressive strengths pre to post freezing and the water desorption coefficient at 180-360 minutes were described using the pore system in the brick.
17. V. Barišić, I. Flanjak, A. Tot, M. Budeč, M. Benšić, A. Jozinović, J. Babić, D. Šubarić, B. Miličević, Đ. Ačkar, 5-hydroxymethylfurfural and acrylamide content of cocoa shell treated with high voltage electrical discharge, Food Control 110/ (2020)
    Abstract

    5-hydroxymethylfurfural (HMF) and acrylamide, as products of Maillard’s reactions, are present in roasted cocoa shell. Since the cocoa shell is increasingly being researched for use in food enrichment due to high fiber content and polyphenols, it is necessary to solve the problem of components that can be harmful to human health. We evaluated the effect of high voltage electrical discharge (HVED) on colour, moisture, HMF and acrylamide content in cocoa shell obtained after roasting cocoa beans. The effects of concentration, frequency and time of cocoa shell treatment were investigated. HVED proved to be a successful method for reducing the content of acrylamide and HMF. In addition, darkening of samples was observed which could mean that further reactions of those components occurred.
18. L. Jakobek, P. Margetić, Š. Kraljević, Š. Ukić, M. Benšić, A. Barron, Adsorption between quercetin derivatives and beta-glucan studied with a novel approach to modeling adsorption isotherms, Applied Sciences 10/ 1637 (2020), 1-16
    Abstract

    Interactions between polyphenols and fibers are important for polyphenol bioactivities, and have been studied in vitro with adsorption process and isotherms. But the theoretical interpretations of adsorption potentially can be affected by the method of isotherm modeling. The aim was to study the interactions between β-glucan and quercetin derivatives (quercetin-3-glucoside, quercetin-3-galactoside, quercetin-3-rhamnoside) by studying adsorption and to potentially improve the modeling of adsorption isotherms. Quercetin derivatives were determined by using spectrophotometric method. Experimental results were modeled with Langmuir, Dubinin-Radushkevich and Hill isotherms using non-linear regression, linear regression and improved non-linear regression. For improved non-linear regression, a code in R program was developed. All quercetin derivatives adsorbed onto the surface of -glucan. Improved non-linear regression gave somewhat lower errors and was more appropriate for adsorption interpretation. According to isotherms obtained with improved regression, it may be suggested that adsorption is higher for rhamnoside and glucoside of quercetin than for quercetin-3-galactoside which agrees with experimental results. Adsorption could be a physical process. The spatial arrangement of OH groups on the glycoside part of quercetin could affect the adsorption. In conclusion, a novel approach using improved non-linear regression has been shown to be a useful novel tool for the adsorption interpretation.
19. V. Barišić, I. Flanjak, M. Kopjar, M. Benšić, A. Jozinović, J. Babić, D. Šubarić, B. Miličević, K. Doko, Đ. Ačkar, Does high voltage electrical discharge treatment induce changes in tannin and fiber properties of cocoa shell?, Foods 9/6 (2020)
    Abstract

    Cocoa shell is a by-product of the chocolate industry that is rich in dietary fiber and bioactive components. In this research, the influence of high voltage electric discharge (HVED) treatment on chemical and physical characteristics of the cocoa shell, i.e., the effects of applied time and frequencies on grinding ability, water binding capacity (WBC), dietary fibers and tannin content was investigated. HVED had a significant influence on the chemical and physical properties of cocoa shell, all of which could be linked to changes in fiber properties. Along with the fiber content, grinding ability and water binding capacity were increased. These properties have already been linked to fiber content and soluble/insoluble fiber ratio. However, this research implies that change in fiber properties could be linked to tannin formation via complexation of other polyphenolic components. Additional research is needed to verify this effect and to establish mechanisms of tannin formation induced by HVED and its influence on fiber quantification.
20. S. Hamedović, M. Benšić, K. Sabo, Estimating the width of a uniform distribution under symmetric measurement errors, Journal of the Korean Statistical Society 49/3 (2020), 822-840
    Abstract

    In this paper we consider the problem of estimating the support of a uniform distribution under symmetric additive errors. The maximum likelihood (ML) estimator is of our primary interest, but we also analyze the method of moments (MM) estimator, when it exists. Under some regularity conditions, the ML estimator is consistent and asymptotically efficient. Errors with Student's t distribution are shown to be a good choice for robustness issues.
21. R. Bušić, M. Benšić, I. Miličević, K. Strukar, Prediction Models for the Mechanical Properties of Self-Compacting Concrete with Recycled Rubber and Silica Fume, Materijals 13/8 (2020)
    Abstract

    The paper aims to investigate the influence of waste tire rubber and silica fume on the fresh and hardened properties of self-compacting concrete (SCC) and to design multivariate regression models for the prediction of the mechanical properties of self-compacting rubberized concrete (SCRC). For this purpose, 21 concrete mixtures were designed. Crumb rubber derived from end-of-life tires (grain size 0.5–3.5 mm) was replaced fine aggregate by 0%, 5%, 10%, 15%, 20%, 25%, and 30% of total aggregate volume. Silica fume was replaced cement by 0%, 5%, and 10% of the total cement mass. The optimal replacement level of both materials was investigated in relation to the values of the fresh properties and mechanical properties of self-compacting concrete. Tests on fresh and hardened self-compacting concrete were performed according to the relevant European standards. Furthermore, models for predicting the values of the compressive strength, modulus of elasticity, and flexural strength of SCRC were designed and verified with the experimental results of 12 other studies. According to the obtained results, mixtures with up to 15% of recycled rubber and 5% of silica fume, with 28 days compressive strength above 30 MPa, were found to be optimal mixtures for the potential future investigation of reinforced self-compacting rubberized concrete structural elements.
22. J. Panak Balentić, A. Jozinović, Đ. Ačkar, J. Babić, B. Miličević, M. Benšić, M. Vladetić, S. Jokić, A. Šarić, Nutritionally improved third generation snacks produced by supercritical CO2 extrusion I. Physical and sensory properties, Journal of food process engineering 42/2 (2019)
    Abstract

    This study was aimed at investigating the possible application of defatted hazelnut, camelina, pumpkin, and hemp cakes (by‐products of edible oil production) in the production of corn snack products, and to use supercritical CO2 as a blowing agent in indirectly expanded snack products. Cakes were added in 3, 6, and 9% proportions. Extrusion was performed in a laboratory single screw extruder and expanded by microwave. The obtained extrudates were evaluated for their physical and sensory properties. For comparison, directly expanded products without supercritical CO2, were produced with the same raw materials. The addition of the by‐product had a significant influence on the expansion ratio, bulk density, fracturability, and crispiness, and all four by‐products were successfully incorporated in the production of sensory acceptable, indirectly expanded snack products, produced by supercritical fluid extrusion. This type of products is interesting for consumers since it can be home‐made and produced without additives or any chemical substances.
23. A. Barron, M. Benšić, K. Sabo, A Note on Weighted Least Square Distribution Fitting and Full Standardization of the Empirical Distribution Function, TEST 27/4 (2018), 946-967
    Abstract

    The relationship between the norm square of the standardized cumulative distribution and the chi-square statistic is examined using the form of the covariance matrix as well as the projection perspective. This investigation enables us to give uncorrelated components of the chi-square statistic and to provide interpretation of these components as innovations standardizing the cumulative distribution values. The norm square of the standardized difference between empirical and theoretical cumulative distributions is also examined as an objective function for parameter estimation. Its relationship to the chi-square distance enables us to discuss the large sample properties of these estimators and a difference in their properties in the cases that the distribution is evaluated at fixed and random points.
24. S. Hamedović, M. Benšić, K. Sabo, P. Taler, Estimating the size of an object captured with error, Central European Journal of Operations Research 26/3 (2018), 771-781
    Abstract

    In many applications we are faced with the problem of estimating object dimensions from a noisy image. Some devices like a fluorescent microscope, X-ray or ultrasound machines, etc., produce imperfect images. Image noise comes from a variety of sources. It can be produced by the physical processes of imaging, or may be caused by the presence of some unwanted structures (e.g. soft tissue captured in images of bones ). In the proposed models we suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error. Here we use two one-dimensional parametric models to construct confidence intervals and statistical tests pertaining to the object size and suggest the possibility of application in two-dimensional problems. Normal and Laplace distributions are used as error distributions. Finally, we illustrate ability of the R-programs we created for these problems on a real-world example.
25. K. Buljan, M. Benšić, M. Vladetić, V. Buljan, S. Butković-Soldo, Functional Carotid Ultrasound Markers of Subclinical Atherosclerosis in Vascular Healthy Women, NEUROSONOLOGY AND CEREBRAL HEMODYNAMICS 14/ (2018), 31-40
26. I. Kosović, M. Benšić, Đ. Ačkar, A. Jozinović, Ž. Ugarčić, J. Babić, B. Miličević, D. Šubarić, Microstructure and cooking quality of barley-enriched pasta produced at different process parameters, Foods and Raw materials 6/2 (2018), 281-290
    Abstract

    Pasta is one of the most popular meals in the world. It is affordable, easy to combine with other foods and easy to cook. Unfortunately, pasta is energy-rich and nutrient-poor. Whole-wheat pasta is somewhat better in nutritional quality, but further improvements may be made. One option is to add different raw materials and specific nutritive components (vitamins, polyphenols, fiber, protein, etc.) to semolina. However, this approach changes its physicochemical properties, e.g. cooking loss, texture, etc., which cannot be disregarded. The current research investigates possibilities for production of barley-enriched pasta with acceptable cooking qualities. To ensure the beneficial health effects of β-glucan, β-glucan-rich barley was selected asa starting material. Pasta enriched with 10–50% β-glucan-rich barley flour was produced in the mini-press and the laboratory extruder and then dried at low, medium and high temperature regimes. Colour, cooking quality and microstructure of the enriched pasta were investigated to determine its acceptability. The research showed that barley-enriched pasta of good cooking quality might be produced by selecting an optimal combination of suitable production parameters for forming and drying.
27. K. Buljan, M. Benšić, V. Buljan, M. Vladetić, S. Butković-Soldo, Functional carotid ultrasound markers of subclinical atherosclerosis in men with cardiovascular risk factors, Southeastern European Medical Journal 1/1 (2017), 19-26
28. J. Flam, D. Gugić, M. Benšić, S. Tomić, J. Rajc, High tumor stroma proportion is a worse prognostic factor in colorectal cancer , ACTA CLINICA CROATICA 56/ (2017)
29. M. Benšić, P. Taler, S. Hamedović, E.K. Nyarko, K. Sabo, LeArEst: Length and Area Estimation from Data Measured with Additive Error, The R Journal 9/2 (2017), 461-473
    Abstract

    This paper describes an R package LeArEst that can be used for estimating object dimensions from a noisy image. The package is based on the simple parametric model for data that are drawn from uniform distribution contaminated by an additive error. Our package is able to estimate the length of the object of interest on a given straight line that intersects it as well as to estimate the object area if it is elliptically shaped. The input data may be a numerical vector as well as an image in JPEG format. In this paper, background statistical models and methods for the package are summarized, and algorithms and key functions implemented are described. Also, examples that demonstrate its usage are provided.
30. M. Benšić, K. Sabo, Uniform distribution width estimation from data observed with Laplace additive error, Journal of the Korean Statistical Society 45/4 (2016), 505-517
    Abstract

    A one-dimensional problem of a uniform distribution width estimation from data observed with a Laplace additive error is analyzed. The error variance is considered as a nuisance parameter and it is supposed to be known or consistently estimated before. It is proved that the maximum likelihood estimator in the described model is consistent and asymptotically efficient and sufficient conditions for its existence are given. The method of moment estimator is also analyzed in this model and compared with the maximum likelihood estimator theoretically and in simulations. Finally, one real-world example illustrates the possibility for applications in two-dimensional problems.
31. M. Benšić, Properties of the generalized nonlinear least squares method applied for fitting distribution to data, Discussiones Mathematicae Probability and Statistics 35/1-2 (2015), 75-94
    Abstract

    We introduce and analyze a class of estimators for distribution parameters based on the relationship between the distribution function and the empirical distribution function. This class includes the nonlinear least squares estimator and the weighted nonlinear least squares estimator which has been used in parameter estimation for lifetime data as well as the generalized nonlinear least squares estimator proposed in Bensic. Sufficient conditions for consistency and asymptotic normality are given. Capability and limitations are illustrated by simulations.
32. K. Buljan, S. Butković-Soldo, D. Jančuljak, D. Kadojić, M. Čandrlić, M. Benšić, V. Buljan, Relationship between Age and Thickness of Carotid Arteries in a Population without Risk Factors for Atherosclerosis, Collegium antropologicum 39/3 (2015), 779-784
33. J. Milić, A. Kvolik, A. Babić Čikeš, I. Labak, M. Benšić, V. Ilakovac, M. Ništ, L. Zibar, M. Heffer, Are There Differences in Students’ School Success, Biorhythm, and Daytime Sleepiness Depending on Their School Starting Times?, Collegium antropologicum 38/3 (2014), 889-893
34. M. Benšić, Fitting distribution to data by a generalized nonlinear least squares method, Communications in statistics-simulation and computation 43/4 (2014), 687-705
    Abstract

    The primary concern is to introduce and illustrate the way of using a generalized nonlinear regression method for the purpose of parameter estimation in the classical parametric independent and identically distributed sample model. It is shown by simulation that the presented estimator has a root mean square error comparable to the maximum likelihood estimator in the model for which it is known that maximum likelihood has excellent properties. As this estimator is based on an empirical distribution function, it is also compared to the maximum goodness-of-fit estimators that minimize Cramer-von Mises and Anderson- Darling empirical distribution statistics and it is shown that it outperforms them in most cases.
35. R. Pavić, P. Margetić, M. Benšić, R. Letica Brnadić, Diagnostic value of US, MR and MR arthrography in shoulder instability, Injury 44/3 (2013), 26-32
36. A. Hunjet, Đ. Parac-Osterman, M. Benšić, Yellow as a domnant tone, Tehnički vjesnik 19/1 (2012), 93-98
37. S. Mihaljević, M. Katičić, Ž. Krznarić, B. Dmitrović, M. Štefanić, Lj. Pinotić, M. Samarđija, M. Benšić, I. Karner, The influence of the different morphological changes on gastric mucosa on somatostatin cell number in antrum mucosa and serum somatostatin, Collegium antropologicum 35/ (2011), 5-8
38. I. Labak, D. Šnajder, M. Kostović Srzentić, M. Benšić, M. Ništ, V. Ilakovac, M. Heffer, Writing and Drawing with Both Hands as Indicators of Hemispheric Dominance, Collegium antropologicum 35/ (2011), 65-71
39. M. Benšić, K. Sabo, Estimating a uniform distribution when data are measured with a normal additive error with unknown variance, Statistics - a Journal of Theoretical and Applied Statistics 44/3 (2010), 235-246
    Abstract

    The problem of estimating the width of a symmetric uniform distribution on the line together with the error variance, when data are measured with normal additive error, is considered. The main purpose is to analyze the maximum likelihood estimator and to compare it with the moment method estimator. It is shown that this two-parameter model is regular so that the maximum likelihood estimator is asymptotically e± ; cient. Necessary and su± ; cient conditions are given for the existence of the maximum likeli- hood estimator. As numerical problems are known to frequently occur while computing the maximum likelihood estimator in this model, useful suggestions for computing the maximum likelihood estimator are also given.
40. M. Pavleković, M. Benšić, M. Zekić-Sušac, Modelling Children's Mathematical Gift By Neural Networks and Logistic Regression, Expert systems with applications 37/10 (2010), 7167-7173
    Abstract

    The purpose of the paper was to extract important features of children’s mathematical gift by using neural networks and logistic regression, in order to create a model that will assist teachers in elementary schools to recognize mathematically gifted children in an early stage, therefore enabling further development and realization of that gift. The initial model was created on the basis of a theoretical background and heuristical knowledge on giftedness in mathematics, including five components: (1) mathematical competencies, (2) cognitive components of gift, (3) personal components that contribute gift development, (4) environmental factors, and (5) efficiency of active learning and exercising methods, as well as grades and out-of-school activities of pupils in the fourth year of elementary school. The three neural network classification algorithms were tested in order to extract the important variables for detecting mathematically gifted children. The best neural network model was selected on the basis of a 10-fold cross-validation procedure. The model was also investigated by the logistic regression. Important predictors detected by two methods were compared and analyzed. The results show that both methods extract similar set of variables as the most important, including grades in mathematics, mathematical competencies of a child regarding numbers and calculating, but also grades in the literature, and environmental factors.
41. K. Sabo, M. Benšić, Border estimation of a disc observed with random errors solved in two steps, Journal of Computational and Applied Mathematics, 229/1 (2009), 16-26
    Abstract

    The problem of estimating the boundary of a uniform distribution on a disc is considered when data are measured with normally distributed additive random error. The problem is solved in two steps. In the first step the domain is subdivided into thin slices and the endpoints of slices are obtained within the framework of a corresponding one-dimensional problem. For the estimations implemented in that step the moment method and the maximum likelihood method are used. As there are numerical problems with calculating the variance of the estimator in the maximum likelihood approach, its good approximation is also given. In the second step the obtained endpoints are used to estimate the boundary using the total least-squares curve fitting procedure. A necessary and sufficient condition for the existence of the total least-squares solution is also given. Finally, simulation results are presented.
42. N. Šarlija, M. Benšić, M. Zekić-Sušac, Comparison procedure in predicting the time to default in behavioral scoring, Expert systems with applications 36/5 (2009), 8778-8788
    Abstract

    The paper deals with the problem of predicting the time to default in credit behavioural scoring. This area opens a possibility of including a dynamic component in behavioural scoring modelling which enables making decisions related to limit, collection and recovery strategies, retention and attrition, as well as providing an insight into the profitability, pricing or term structure of the loan. In this paper we compare survival analysis and neural networks in terms of modelling and results. The neural network architecture is designed such that its output is comparable to the survival analysis output. Six neural network models were created, one for each period of default. A radial basis neural network algorithm was used to test all six models. The survival model used a Cox modelling procedure. Further, different performance measures of all models were discussed since even in highly accurate scoring models, misclassification patterns appear. A systematic comparison ‘ 3+2+2’ procedure is suggested to find the most effective model for a bank. Additionally, the survival analysis model is compared to neural network models according to the relative importance of different variables in predicting the time to default. Although different models can have very similar performance measures they may consist of different variables. The dataset used for the research was collected from a Croatian bank and credit customers were observed during a twelve-month period. The paper emphasizes the importance of conducting a detailed comparison procedure while selecting the best model that satisfies the users' interest.
43. D. Marković, D. Jukić, M. Benšić, Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, Journal of Computational and Applied Mathematics, 228/1 (2009), 304-312
    Abstract

    This paper is concerned with the parameter estimation problem for the three-parameter Weibull density which is widely employed as a model in reliability and lifetime studies. Our approach is a combination of nonparametric and parametric methods. The basic idea is to start with an initial nonparametric density estimate which needs to be as good as possible, and then apply the nonlinear least squares method to estimate the unknown parameters. As a main result, a theorem on the existence of the least squares estimate is obtained. Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality.
44. H. Lepeduš, H. Fulgosi, M. Benšić, V. Cesar, Efficiency of the photosynthetic apparatus in developing needles of Notway spruce (Picea abies L. Karst), Acta Biologica Hungarica 59/2 (2008), 217-232
45. D. Jukić, M. Benšić, R. Scitovski, On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution, Computational Statistics & Data Analysis 52/9 (2008), 4502-4511
    Abstract

    The problem of nonlinear weighted least squares fitting of the three-parameter Weibull distribution to the given data (wi,ti,yi), i=1,…,n, is considered. The part wi>0 of the data stands for the data weights. It is shown that the best least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) 0<t1<t2<⋯<tn and (ii) 0<y1<y2<⋯<yn<1. To support this, an illustrative numerical example is given.
46. R. Pavić, M. Pavić, O.K. Tot, M. Benšić, M. Heffer, Side distinct sciatic nerve recovery differences between rats and mice, Somatosensory & Motor Research 25/3 (2008), 163-170
47. M. Benšić, K. Sabo, Border Estimation of a Two-dimensional Uniform Distribution if Data are Measured with Additive Error, Statistics - a Journal of Theoretical and Applied Statistics 41/ (2007), 311-319
    Abstract

    The paper considers estimation of the boundary of an elliptical domain when the data without a measurement error are distributed uniformly on this domain but are superimposed by random errors. The problem is solved in two phases. In the first phase the domain is subdivided into thin slices and the endpoints of these slices are estimated within the framework of a corresponding one-dimensional problem. In the second phase the estimated endpoints are used to estimate the boundary using the total least squares curve fitting procedure
48. A. Hunjet, Đ. Parac-Osterman, M. Benšić, Doživljaj tona boje na akromatskim podlogama, Tehnički glasnik 1/ (2007), 38-43
49. M. Benšić, K. Sabo, Estimating the width of a uniform distribution when data are measured with additive normal errors with known variance, Computational Statistics & Data Analysis 51/ (2007), 4731-4741
    Abstract

    The problem of estimating the width of the symmetric uniform distribution on the line when data are measured with normal additive error is considered. The main purpose is to discuss the efficiency of the maximum likelihood estimator and the moment method estimator. It is shown that the model is regular and that the maximum likelihood estimator is more efficient than the moment method estimator. A sufficient condition is also given for the existence of both estimators.
50. N. Šarlija, M. Benšić, M. Zekić-Sušac, Logistic refression, survival analysis and neural networks in modeling customer credit scoring, WSEAS Transactions on Business and Economics 3/3 (2006), 64-70
51. A. Hunjet, Đ. Parac-Osterman, M. Benšić, Utjecaj boje okoline na doživljaj žutog i plavog tona, Tekstil 55/3 (2006), 121-126
52. M. Benšić, N. Šarlija, M. Zekić-Sušac, Modeling Small Business Credit Scoring Using Logistic Regression, Neural Networks, and Decision Trees, Intelligent Systems in Accounting, Finance and Management 13/3 (2005), 133-150
53. M. Zekić-Sušac, M. Benšić, N. Šarlija, Selecting neural network architecture for investment profitability predictions, Journal of Information and Organizational Sciences 29/2 (2005), 83-95
54. Ž. Vukšić-Mihaljević, M. Benšić, D. Begić, G. Lauc, B. Hutinec, V. Čandrlić, V. Todorović, Combat Related Posttraumatic Stress Disorder Among Croatian Veterans: The Causal Models of Symptom Clusters, The European Journal of Psychiatry 18/4 (2004), 197-208
55. M. Benšić, M. Pavleković, Matematički časopis kao učiteljev izvor ideja za suvremenijom organizacijom nastave matematike, Život i škola 9/1 (2003), 39-49
56. Z. Bohaček, N. Šarlija, M. Benšić, Upotreba kredit skoring modela za ocjenjivanje kreditne sposobnosti malih poduzetnika, Ekonomski pregled 54/7/8 (2003), 565-580
57. S. Mihaljević, I. Karner, B. Dmitrović, M. Benšić, N. Mičunović, A. Včev, B. Škurla, M. Katičić, Hormonska regulacija želučane sekrecije i helicobacter pylori, Liječnički vjesnik 124/1 (2002), 13-16
58. M. Benšić, N. Šarlija, Influence of entrepreneur's educational background and experience on number of employees, Mathematical Communications - Supplement 1/1 (2001), 121-126
59. M. Benšić, N. Šarlija, Analiza utjecaja na broj uposlenih u poduzećima hrvatskih poduzetnika, Ekonomski pregled 51/11-12 (2000), 1229-1238
60. Ž. Vukšić-Mihaljević, N. Mandić, M. Benšić, S. Mihaljević, Postraumatic stress disorder among Croatian veterans: A causal model, Psychiatry and Clinical Neurosciences 54/ (2000), 625-636
61. N.N. Leonenko, M. Benšić, On estimation of regression coefficients of long memory random fields observed on the arrays, Random operators and stochastics equations 5/3 (1997), 237-252
    Abstract

    We study some problems of the parameter inference which are in connection with long memory homogeneous and isotropic random fields. We present the asymptotic behavior for the correlation matrix and the limit distributions of the LSE for regression coefficients in some regression models with long memory Gaussian and non-Gaussian errors.
62. N.N. Leonenko, M. Šilac-Benšić, On the asymptotic distributions of least square estimations in a regression model with singular erors, Dopovidi NAS of Ukraine 7/ (1997), 26-31
63. N.N. Leonenko, M. Benšić, Asymptotic properties of the LSE in a regression model with long-memory Gaussian and non-Gaussian stationary errors, Random operators and stochastics equations 4/1 (1996), 17-32
    Abstract

    We study some problems of the parameter inference which a in connection with long-memory covariance stationary processes. We present the asymptotic behavior for the variance and the limit distributions of the LSE for the regression coefficients in some cases of long-memory, stationary, Gaussian and non-Gaussian errors.
64. N.N. Leonenko, M. Šilac-Benšić, On estimation of regression coefficients in the case of long-memory noise, Theory of Stochastic Processes 18/3-4 (1996), 108-119
    Abstract

    In this paper we consider some asymptotic properties of the LSE of continuous time and non-Gaussian long-memory errors. The precise description of the model we have been working with is given through the second section.
65. B. Dukić, D. Francišković, D. Jukić, R. Scitovski, M. Benšić, Strategije otplate zajma, Financijska teorija i praksa (1994), 15-26
66. M. Šilac, Otplata zajma varijabilnim anuitetima, Economic analysis and worker's management 23/2 (1989), 185-197

1. M. Benšić, P. Taler, E.K. Nyarko, Statistical estimation of the object’s area from the image contaminated with additive noise, 15th Iberian Conference on Information Systems and Technologies (CISTI), Seville, Spain, 2020, 1-6
   Abstract

   Area estimation of circular or ellipsoidal object on an image is a current issue in computer vision. Several methods that address this problem have been previously presented, but it turned out that they do not give satisfactory results when dealing with noisy images. As part of the research presented in this paper, a statistical model for estimating the width of uniform distribution for data contaminated with additive error was applied in order to approach the mentioned problem in an innovative manner. Initially, a method for length estimation of intersection of an object with an arbitrary line has been developed. It is possible to estimate the set of object’s edge points using this method. Further, a circle or an ellipse is fitted in that set of points and its area is calculated, which approximates the area of the object itself. It is also possible to estimate the area of a circular or ellipsoidal object represented by a set of points in the plane.The presented method was implemented and publicly released as a package for the programming language R. The method has been extensively tested on the problem of estimating the area of objects recorded using RGB-D camera. Different noise levels were added to the captured images, and estimation results were compared with the ones obtained by several established methods. The test results showed that the method presented in this paper gives qualitatively the best results of area estimation when dealing with noisy images.
2. P. Taler, S. Hamedović, M. Benšić, E.K. Nyarko, LeArEst - The Software for Border and Area Estimation of Data Measured with Additive Error, 59th International Symposium ELMAR-2017, Zadar, 2017, 259-263
   Abstract

   This paper proposes a solution to the problem of estimating object dimensions from a noisy image. Image noise can be produced by the physical processes of imaging, or can be caused by the presence of some unwanted structures (e.g. soft tissue captured in X-ray images of bones). We suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error having normal or Laplace distribution. The software for border estimation of an object registered in such manner has been developed, and brief description of its key functions is given. The software is able to estimate the borders of an object on a given line that intersects it, as well as to estimate its area. Its input data may be numerical data, as well as images in JPEG format.
3. M. Zekić-Sušac, N. Šarlija, M. Benšić, Insolvency prediction by neural networks, 12th International Conference on Operational Research, Pula, Croatia, 2009, 175-188
4. M. Benšić, D. Jankov Maširević, Parameter estimation for a three-parameter Weibull distribution - a comparative study, 12th International Conference on Operational Research, Pula, Croatia, 2008, 159-164
5. N. Šarlija, M. Benšić, M. Zekić-Sušac, A neural network clasification of credit applicants in consumer credit scoring, IASTED International Conference on Artificial Intelligence and Applications, part of the 24th Multi-Conference on Applied Informatics, 2006, Innsbruck, 2006, 205-210
6. N. Šarlija, M. Benšić, M. Zekić-Sušac, Modeling customer revolving credit scoring using logistic regression, survival analysis and neural networks, 7th WSEAS International Conference on Neural Networks, Cavtat, 2006, 164-169
   Abstract

   The aim of the paper is to discuss credit scoring modeling of a customer revolving credit depending on customer application data and transaction behavior data. Logistic regression, survival analysis, and neural network credit scoring models were developed in order to assess relative importance of different variables in predicting the default of a customer. Three neural network algorithms were tested: multilayer perceptron, radial basis and probabilistic. The radial basis function network model produced the highest average hit rate. The overall results show that the best NN model outperforms the LR model and the survival model. All three models extracted similar sets of variables as important. Working status and client's delinquency history are the most important features for customer revolving credit scoring on the observed dataset.
7. S. Pfeifer, M. Benšić, N. Šarlija, An insight into using entrepreneurship intentions as predictor of entrepreneurial behavior, The Entrepreneurship - Innovation - Marketing Interface, Karlsruhe, 2005, 89-108
   Abstract

   Entrepreneurial behavior is vital for economic recovery and growth. Potential for business start-ups or potential for wealth creating behavior is a prerequisite of any economic development. Permanent supply of the new venture creators or entrepreneurship career seekers can be supported through identification of what and how many influences are critical for the emergence of the entrepreneurial intentions. The research examines well documented and theoretically consistent intent approach, while methodologically it tests the robustness of the structural equation model. This model enables measurement of direct and indirect influences on entrepreneurial intentions and behavior. A sample of Croatian final year students of economics is used to investigate intentions of the future labor force for choosing the entrepreneurial self-owned business start-up as a career option. Consistent with other studies examining the influence of the intentions on behavior, it was hypothesized that the more favorable the attitude and perceived norms about entrepreneurial behavior are and the greater the perceived feasibility (control) of the entrepreneurial act is, the stronger the intention to perform the behavior will be. Furthermore, the greater the degree to which the behavior can be controled, the greater the influence of the knowledge about the intentions to perform the defined behavior. The research provides several benefits. In particular, recognition of the critical antecedents of the entrepreneurial behavior and the empirical testing of the participant prior to her/his choice enables policy makers to determine propensity of entrepreneurial potential transition into an entrepreneurial performance. The findings of the study provide evidence that the university environment could play a more important role in entrepreneurship encouragement and support. University programs designers would get a clear message about the perception and expectations that future labor force has about entrepreneurship ; therefore, more efficient program curricula could be implemented in the university education. Empirical testing of the participant prior to his or her career choice enables one to determine whether perception of the effects of government entrepreneurship reforms are ecouraging or not, and whether the overall community is fostering or hindering entrepreneurism. Another benefit of this study would be to ensure that supportive measures hit the right targets in the process of using the entrepreneurial vehicle as the crucial one for economic development.
8. N. Šarlija, M. Benšić, Z. Bohaček, Customer revolving credit – how the economic conditions make a difference, Credit Scoring & Credit Control IX, Edinburgh, 2005
   Abstract

   The aim of this paper is to discuss credit scoring modeling of a customer revolving credit depending on customer application data and transaction behavior data influenced by specific economic conditions that exist in Croatia. Since Croatia is a country in transition with war consequences, changes in political, institutional and social systems and, above all, with specific economic conditions characterized by slow economy, a high unemployment rate and a relatively low personal income, it is assumed that this influences credit behavior of customers and, as a consequence, a composition of credit scoring models. For instance, it has been shown that a small business credit scoring model developed in Croatia is influenced by economic conditions. The data set for our research consisted of 50,000 customer accounts (application data and transaction data) in Croatia over the period of 12 months. We have developed a logistic credit scoring model and a survival-based credit scoring model in order to assess the relative importance of different variables in predicting default as well as profitability of a customer. The paper analyzes influences of economic conditions on credit scoring modeling.
9. N. Šarlija, M. Benšić, Z. Bohaček, Multinomial model in consumer credit scoring, 10th International Conference on Operational Research KOI 2004, Trogir, 2004, 193-202
   Abstract

   Credit scoring is a process of determing how likely applicants are to default withe their repayments. It has been used in consumer lending for more then three decades. Data sample of consumer credits used in this research is divided into three groups - good, poor and bad. The aim of this paper is to explore the possibility of using poor applicants in developing a credit scoring model. In ordet to accomplish this, multinomial models have been developed. Also, for the purpose of obtaining results as good as possible, three binomial models have been built. These models are compared according to significant variables and classification accuracy after which the best model is extracted.
10. M. Zekić-Sušac, N. Šarlija, M. Benšić, Small business credit scoring: A comparison of logistic regression, neural network and decision tree models, 26th International Conference on Information Tehnology Interfaces, Cavtat, Dubrovnik, 2004, 265-270
    Abstract

    The paper compares the models for small business credit scoring developed by logistic regression, neural networks, and CART decision trees on a Croatian bank dataset. The models obtained by all three methodologies were estimated ; then validated on the same hold-out sample, and their performance is compared. There is an evident significant difference among the best neural network model, decision tree model, and logistic regression model. The most successful neural network model was obtained by the probabilistic algorithm. The best model extracted the most important features for small business credit scoring from the observed data.
11. S. Mihaljević, M. Katičić, B. Dmitrović, I. Karner, A. Včev, V. Borzan, S. Canecki, Ž. Vranješ, V. Prus, J. Barbić, M. Benšić, The Influence of Stomach Mucosa Morphological Changes on Somatostatin Cell Number in Atrum Mucosa, 11th International Conference on Ulcer Research, Dubrovnik, 2003, 307-312
12. M. Benšić, Z. Bohaček, N. Šarlija, M. Zekić-Sušac, Neural Network-and-Logit-Based Modeling Strategy for Small Business Credit Scoring, International Conference Forecasting Financial Markets : Advances for Exchange Rates, Interest Rates and Asset Management, London, 2002
    Abstract

    Credit scoring has been so far investigated using both logistic regression and neural networks mostly for the purpose of comparing the accuracy of two methods (Desai et al, 1997 ; West, 2000), using commonly recognized credit scoring models. However, due to specific characteristics of small business loans, the importance of selecting different variables from other company loans is emphasized by practitioners and researchers (Feldman, 1997). Specific economic conditions, especially in transitional countries, that also influence model effectiveness, emphasize a close relationship between methodology accuracy and variable selection. This paper investigates such relationship by performing a neural network forward cross-validation modeling strategy based on hit rates, logit univariate and logit forward selection analysis. Comparing the accuracy of both methods, the system is able to extract the best model for the given data. Tested on a Croatian small business loans dataset, it proposes the set of important features for credit scoring in that specific economic environment.
13. M. Benšić, Đ. Borozan, Nonlinearity in the foreign-exchange market: the application of close returns analysis, 7th International Conference on Operational Research KOI 1998, Rovinj, 1999, 311-316
14. M. Benšić, R. Scitovski, Određivanje intervala povjerenja za neke specijalne nelinearne regresije, 6th International Conference on Operational Research KOI 1996, Rovinj, 1996, 87-92
    Abstract

    U radu se analiziraju rezultati primjene metode linearizacije na određivanje intervala i područja povjerenja za nepoznate parametre logističke i 3-parametarske eksponencijalne regresije.

1. M. Benšić, D. Grahovac, D. Mihalčić, Linearna regresija kroz primjer, Osječki matematički list 23/2 (2023), 115-131
   Abstract

   U radu je prezentirana osnovna ideja linearne regresije. Glavni pojmovi objašnjeni su intuitivno. Naglasak je na konkretnom primjeru gdje je cijena automobila modelirana na temelju njegovih osnovnih karakteristika. Model je izrađen na temelju stvarnih podataka o rabljenim automobilima u Hrvatskoj.
2. M. Benšić, G. Benšić, Kamatni račun, Osječki matematički list 11/2 (2011), 113-126
   Abstract

   U radu je prezentiran jednostavan metodološki pristup u obradi kamatnog računa temeljen samo na dvjema ključnim formulama te razumijevanju i primjeni principa jednostavnog i složenog ukamaćivanja. Pokazano je da izvedene formule za jednostavno i složeno ukamaćivanje određuju funkciju rasta kapitala po razlicitim modelima kapitalizacije što ukazuje na potrebu strogog poštovanja odabranog principa ukamaćivanja u svakom pojedinom problemu. Navedeni su neki primjeri iz hrvatskih udžbenika matematike u kojima se o tome ne vodi računa te se u jednom zadatku koriste oba principa. Ovakvi i slični zadaci mogu biti uzrok zbrci koju u glavi imaju učenici kada pokušavaju naučiti kamatni račun.
3. M. Benšić, Jedna igra na sreću, Osječki matematički list 1/ (2001), 5-8
4. M. Benšić, M. Crnjac, Optimalan Lp procjenitelj nepoznatih parametara regresijskog modela, Ekonomski vjesnik 10/1 (1998), 71-74
5. M. Benšić, Confidence regions and intervals in nonlinear regression, Mathematical Communications 2/ (1997), 71-76
6. M. Benšić, Asymptotic distributions of least square estimations in a regression model with singular errors, Mathematical Communications 1/2 (1996), 33-38
7. M. Šilac-Benšić, Problemi optimalnog izbora, Ekonomski vjesnik 2/5 (1992), 327-328
8. R. Scitovski, M. Šilac, D. Francišković, Problemi i nesporazumi u primjeni financijske matematike, Privreda 33/ (1989), 243-257

1. M. Benšić, D. Grahovac, I. Papić, N. Šuvak, Primijenjena statistika, Sveučilište Josipa Jurja Strossmayera u Osijeku - Fakultet primijenjene matematike i informatike, Osijek, 2025.
2. M. Benšić, N. Šuvak, Uvod u vjerojatnost i statistiku, Sveučilište J.J. Strossmayera, Odjel za matematiku, Osijek, 2014.
3. M. Benšić, N. Šuvak, Primijenjena statistika 2013, Sveučilište J.J. Strossmayera, Odjel za matematiku, Osijek, 2013.

1. M. Benšić, D. Grahovac, I. Papić, N. Šuvak, Primijenjena statistika - baze (2025)
2. M. Benšić, K. Sabo, P. Taler, S. Hamedović, LeArEst softverski paket za R (2017)
   Abstract

   Package provides methods for estimating borders of uniform distribution on the interval (one-dimensional) and on the elliptical domain (two-dimensional) under measurement errors. For one-dimensional case, it also estimates the length of underlying uniform domain and tests the hypothesized length against two-sided or one-sided alternatives. For two-dimensional case, it estimates the area of underlying uniform domain. It works with numerical inputs as well as with pictures in JPG format.

1. A. Barron, M. Benšić, K. Sabo, Standardizing the Empirical Distribution Function Yields the Chi-Square Statistic (2016)
   Abstract

   Standardizing the empirical distribution function yields a statistic with norm square that matches the chi-square test statistic. To show this one may use the covariance matrix of the empirical distribution which, at any finite set of points, is shown to have an inverse which is tridiagonal. Moreover, a representation of the inverse is given which is a product of bidiagonal matrices corresponding to a representation of the standardization of the empirical distribution via a linear combination of values at two consecutive points. These properties are discussed also in the context of minimum distance estimation

Projects

• The optimization and statistical models and methods in recognizing properties of data sets measured with errors, (Career development of young researchers – training of new PhDs, founded by Croatian Science Foundation, 2017-2021)
• Exploration of optimization and estimation properties of Generalized method of moments and Nonlinear least squares (University of Osijek,  2016)
• Statistical aspects of estimation problem in nonlinear parametric models (2006-2013, Croatian Ministry of Science)
• Statistical aspects of parameter identification problems (2001-2006, Croatian Ministry of Science)
• Incentive project for young scientists “Statistical aspects of the parameter identification problems” (1998-2000, Croatian Ministry of Science:)

Participation  in work of the following projects 

• Developing a Conceptual Framework for SME Resilience Using Effectuation Theory, researcher. Leader: Nataša Šarlija (founded by Croatian Science Foundation, 2025-2028)
• Stohastički modeli i primjene (STOMP), Institucionalni istraživački projekt, Voditelj: Ivan Papić 2025.-2029.
• The characterization and modeling of radon concentration distribution in Montenegrin schools and kindergartens, researcher. Leader: Pero Vukotić, academician, CANU (Montenegrin Academy of Sciences and Arts) (founded by CANU, 2025)
• Oleogels as Nutritive Improvers of Chocolate and Sweet Spreads, researcher. Leader: Đurđica Ačkar (founded by Croatian Science Foundation, 2023-2027)
• “Regional Science Centre of Pannonian Croatia” (J.J. Strossmayer University of Osijek – Ministry of Regional Development and EU Funds), 2022- 2024.
• “Development and application of the advanced building materials for construction of healthy buildings: protection from non-ionizing radiation”, (Faculty of Civil Engineering and Architecture, J. J. Strossmayer University of Osijek – European Regional Development Fund) – Project coordinator (MATHOS) (2020-2022)
• The optimization and statistical models and methods in recognizing properties of data sets measured with errors, researcher, leader: Rudolf Scitovski (founded by Croatian Science Foundation, 2017-2021)
• Limiting behavior of intermittent processes and diffusions, researcher, Project coordinator: Danijel Grahovac (UNIOS – ZUP 2018 – Youth Research Projects)
• Frakcionalne Pearsonove difuzije, researcher, leader: Nenad Šuvak (founded by  University J.J. Strossmayer in Osijek, 2015-2016)
• Stanična i tkivna diferencijacija tijekom razvoja biljnih organa, researcher, leader: Vera Cesar (founded by MZOS, 2007.-2013. )
• Posttraumatski stresni poremećaj djece ratnh veterana: kauzalni model, konzultant
  leader: doc.dr.sc. Ž. Vukšić-Mihaljević (founded by MZOS, 2001-2006)
• Parameter identification problem in mathematical models, researcher
  leader: prof.dr.sc. R. Scitovski (founded by MZOS, 1996-2000)
• Teorijske i institucionalne pretpostavke poduzetničke ekonomije, istraživač
  leader: prof.dr.sc. S. Singer (1991.-1996.)
• Theory of probability and mathematical statistics, researcher
  leader: prof.dr.sc. N. Sarapa (1991-1996)
• Zakon vrijednosti u funkciji upravljanja razvojem, istraživač
  leader: prof.dr.sc. S. Singer (1986-1990)

Professional Activities

Mathematical Communications

Osječki matematički list

• Member of the Program Committee of the 8th Croatian Mathematical Congress, Osijek, Jul 2 – 5, 2024
• Member of the Program Committee of the ISCCRO’18: The 2nd International Statistical Conference in CROatia, 10-11 May, 2016, Opatija, Croatia
• Member of the Program Committee of  the ISCCRO’16: The 1st International Statistical Conference in CROatia, 05-06 May, 2016, Zagreb, Croatia
• Member of the Program Committee of the International Symposium Biomedical Informatics, Osijek, 2014.
• Member of the Organizing Committee of the International Colloquiums Mathematics and Children (Osijek 2007-2017)
• Member of the Organizing and Program Committee of the 18th European Young Statisticians Meeting
• Chairman of the Organizing Committee of the 4th Croatian Mathematical Congress, Osijek, June 17-20, 2008

Refereeing/Reviewing (Selection)

Mathematical Communications
Communications in Statistics – Theory and Methods
Computational Statistics & Data Analysis
IEEE Transactions on Reliability
Inteligent Systems in Accounting, Finance and Management
Osječki matematički list
Matematički kolokvijum (MAT-KOL), Banja Luka, ISSN 0354-6969, stručno-metodički časopis

AMS Mathematical Review

• … -2026 – Head of the Probability, Mathematical Statistics and Data Science Research Group
• 2013-2017 – Head of the Department of Mathematics, University of Osijek
• 2012-2013 – Member of the University board for quality assurance in higher education
• 2008-2013 – Substitute Head of the Department of Mathematics, University of Osijek
• 2008-2013 – member of the committee for teacher credentialing (Education and Teacher Training Agency)
• 2005-2011 – Head of the Dept. of Mathematics board for quality assurance in higher education
• 2001-2008 – Assistant Head of the Department of Mathematics, University of Osijek
• 2000–2004 – Head of the Mathematical Colloquium in Osijek

Teaching

Konzultacije (Office Hours):

Nakon termina nastave kolegija ili po dogovoru.

Kontaktirati me možete putem emaila.

Aktualna nastava:

Multivarijatna analiza (Multivariate Analysis), Fakultet primijenjena matematike i informatike

Statistika (Statistics), Fakultet primijenjena matematike i informatike

Uvod u vjerojatnost i statistiku  (Introduction to Probability and Statistics), Fakultet primijenjena matematike i informatike

Planiranje eksperimenata i obrada rezultata (Doktorski studij, Prehrambeno tehnološki fakultet Osijek)

Primijenjena multivarijatna statistika (Applied Multivariate Statistics) (Doktorski studij, Građevinski i arhitektonski fakultet Osijek)

Usmeni ispiti

Studenti koji su ostvarili pravo pristupanja usmenom ispitu trebaju odabrati termin i  prijaviti svoj dolazak najkasnije 7 dana prije odabranog termina korištenjem poveznice navedene ispod ovog odjeljka. Termini su navedeni na istoj poveznici. Naglašavam da je potrebno prijaviti ispit i preko ISVU sustava da bih mogla upisati ocjenu.  Ukoliko je prijavljeno pristupanje usmenom uspitu za jedan termin, eventualnu ponovnu prijavu moguće je napraviti nakon  14 dana.

 Poveznica za prijavu usmenih ispita 

Materijali:

Primijenjena statistika, 2025 (udžbenik)

Uvod u vjerojatnost i statistiku (udžbenik)

Projekt u nastavi matematike srednjih škola

Buffonov pokus u nastavi matematike

Nastava koju sam izvodila (Teaching experiance)

Na Odjelu za matematiku:

Uvod u vjerojatnost i statistiku (Introduction to Probability and Statistics)

Analiza vremenskih nizova (Time Series Analysis)

Statistički praktikum (Stat Labs)

Vjerojatnost (Probability)

Slučajni procesi (Random Processes)

Metodika nastave matematike 1

Metodika nastave matematike 2

Na ostalim sastavnicama Sveučilišta u Osijeku

Statistika (Statistics), Sveučilišni preddiplomski studij kineziologije

Matematika i statistika (Doktorski studij, Strojarski fakultet, Slavonski Brod)

Matematika 1, Matematika 2 (Ekonomski fakultet Osijek)

Teorijska statistika (Ekonomski fakultet Osijek)

Matematika 1, Matematika 2 (Prehrambeno tehnološki fakultet Osijek)

Primijenjena statistika (Građevinski fakultet Osijek)

Primijenjena statistika (Prehrambeno tehnološki fakultet Osijek)

Statistika (Učiteljski fakultet Osijek)

Personal

• Birth year:  1961
• Birthplace: Đakovo, Croatia
• Citizenship: Croatian
• Family: Married with two children (Tin, Anja)