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
R. Pavić, M. Pavić, O.K. Tot, M. Benšić, M. Heffer-Lauc, Side distinct sciatic nerve recovery differences between rats and mice, Somatosensory & Motor Research 25/3 (2008), 163-170M. 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 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
A. Hunjet, Đ. Parac-Osterman, M. Benšić, Doživljaj tona boje na akromatskim podlogama, Tehnički glasnik 1 (2007), 38-43M. 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
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.
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), 64-70A. Hunjet, Đ. Parac-Osterman, M. Benšić, Utjecaj boje okoline na doživljaj žutog i plavog tona, Tekstil 55/3 (2006), 121-126M. 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), 133-150M. Zekić-Sušac, M. Benšić, N. Šarlija, Selecting neural network architecture for investment profitability predictions, Journal of Information and Organizational Sciences 29/2 (2005), 83-95Ž. 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), 197-208M. Benšić, M. Pavleković, Matematički časopis kao učiteljev izvor ideja za suvremenijom organizacijom nastave matematike, Život i škola 9/1 (2003), 39-49Z. Bohaček, N. Šarlija, M. Benšić, Upotreba kredit skoring modela za ocjenjivanje kreditne sposobnosti malih poduzetnika, Ekonomski pregled 54/7/8 (2003), 565-580S. 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), 13-16M. Benšić, N. Šarlija, Influence of entrepreneur's educational background and experience on number of employees, Mathematical Communications - Supplement 1/1 (2001), 121-126M. Benšić, N. Šarlija, Analiza utjecaja na broj uposlenih u poduzećima hrvatskih poduzetnika, Ekonomski pregled 51/11-12 (2000), 1229-1238Ž. Vukšić-Mihaljević, N. Mandić, M. Benšić, S. Mihaljević, Postraumatic stress disorder among Croatian veterans: A causal model, Psychiatry and Clinical Neurosciences 54 (2000), 625-636N.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 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.
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), 26-31N.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 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.
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 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.
B. Dukić, D. Francišković, D. Jukić, R. Scitovski, M. Benšić, Strategije otplate zajma, Financijska teorija i praksa (1994), 15-26M. Šilac, Otplata zajma varijabilnim anuitetima, Economic analysis and worker's management 23/2 (1989), 185-197Refereed Proceedings
- 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
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.
- 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
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.
- M. Zekić-Sušac, N. Šarlija, M. Benšić, Insolvency prediction by neural networks, 12th International Conference on Operational Research, Pula, Croatia, 2009, 175-188
- 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
- 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
- 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
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.
- 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
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.
- N. Šarlija, M. Benšić, Z. Bohaček, Customer revolving credit – how the economic conditions make a difference, Credit Scoring & Credit Control IX, Edinburgh, 2005
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.
- N. Šarlija, M. Benšić, Z. Bohaček, Multinomial model in consumer credit scoring, 10th International Conference on Operational Research KOI 2004, Trogir, 2004, 193-202
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.
- 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
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.
- 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
- 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
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.
- 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
- M. Benšić, R. Scitovski, Određivanje intervala povjerenja za neke specijalne nelinearne regresije, 6th International Conference on Operational Research KOI 1996, Rovinj, 1996, 87-92
U radu se analiziraju rezultati primjene metode linearizacije na određivanje intervala i područja povjerenja za nepoznate parametre logističke i 3-parametarske eksponencijalne regresije.
Others
- M. Benšić, G. Benšić, Kamatni račun, Osječki matematički list 11/2 (2011), 113-126
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.
- M. Benšić, Jedna igra na sreću, Osječki matematički list 1 (2001), 5-8
- M. Benšić, M. Crnjac, Optimalan Lp procjenitelj nepoznatih parametara regresijskog modela, Ekonomski vjesnik 10/1 (1998), 71-74
- M. Benšić, Confidence regions and intervals in nonlinear regression, Mathematical Communications 2 (1997), 71-76
- M. Benšić, Asymptotic distributions of least square estimations in a regression model with singular errors, Mathematical Communications 1/2 (1996), 33-38
- M. Šilac-Benšić, Problemi optimalnog izbora, Ekonomski vjesnik 2/5 (1992), 327-328
- R. Scitovski, M. Šilac, D. Francišković, Problemi i nesporazumi u primjeni financijske matematike, Privreda 33 (1989), 243-257
Books
- M. Benšić, N. Šuvak, Uvod u vjerojatnost i statistiku, Sveučilište J.J. Strossmayera, Odjel za matematiku, Osijek, 2014.
- M. Benšić, N. Šuvak, Primijenjena statistika, Sveučilište J.J. Strossmayera, Odjel za matematiku, Osijek, 2013.
Softwares
- M. Benšić, K. Sabo, P. Taler, S. Hamedović, LeArEst softverski paket za R (2017)
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.
Technical Reports
- A. Barron, M. Benšić, K. Sabo, Standardizing the Empirical Distribution Function Yields the Chi-Square Statistic (2016)
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
Leader of the following projects
University J.J. Strossmayer in Osijek:
Exploration of optimization and estimation properties of Generalized method of moments and Nonlinear least squares (2016)
Croatian Ministry of Science:
Statistical aspects of estimation problem in nonlinear parametric models (2006-2013)
Statistical aspects of parameter identification problems (2001-2006)
Poticajni projekt za mlade znanstvenike "Statistički aspekti problema identifikacije parametara" (1998-2000)
Participation in work of the following projects
- "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
Editorial Boards
Mathematical Communications
Osječki matematički list
Matematički kolokvijum (MAT-KOL), Banja Luka, ISSN 0354-6969, stručno-metodički časopis
Committee Memberships
- Member of the Program Committee of ISCCRO’18: The 2nd International Statistical Conference in CROatia, 10-11 May, 2016, Opatija, Croatia
- Member of the Program Committee of 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
Selected Service Activities
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
Nastava (Teaching)
Konzultacije (Office Hours):
Nakon termina nastave kolegija ili po dogovoru.
Kontaktirati me možete putem emaila.
Aktualna nastava:
Multivarijatna analiza (Multivariate Analysis), Odjel za matematiku
Statistika (Statistics), Odjel za matematiku
Vjerojatnost i statistika (Probability and Statistics), Građevinski i arhitektonski fakultet Osijek
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
Prijedlog tema diplomskih radova na Odjelu za matematiku:
- Visokodimenzionalni linearni modeli i LASSO
- Modeliranje razlika u razlikama
- Regresija vremenskog niza
- Statistička analiza usklađenosti ocjenjivača
- Moguće su i druge teme u dogovoru sa zainteresiranim studentom
Materijali:
Primijenjena statistika (udžbenik, baze podataka)
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)