Mirta Benšić


AVM6252 1 200x300 2 Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸
phone: +385-31-224-800
fax: +385-31-224-801
email:  mirta @ mathos.hr
office:  25 (first floor)

Google Scholar profil


Research Interests

Statistical theory (estimators - asymptotic properties)
Statistical applications (medical statistics, econometrics)


PhD in  Mathematics,  University of Zagreb , 1997.
MSc in Mathematics,  University of Zagreb , 1990.
BSc in Mathematics and Physics, University of Osijek, Croatia, 1985.


Journal Publications

  1. 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)
    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.
  2. 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
    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.
  3. 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
    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.
  4. 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
  5. 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
    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.
  6. 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
  7. 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)
  8. 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
    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.
  9. 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
    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.
  10. 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
    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.


  • 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 (as a researcher or consultant) in work of the following projects:

The optimization and statistical models and methods in recognizing properties of data sets measured with errors, leader: Rudolf Scitovski (founded by Croatian Science Foundation, 2017-2021)

Frakcionalne Pearsonove difuzije, leader: Nenad Šuvak (founded by  University J.J. Strossmayer in Osijek, 2015-2016)

Stanična i tkivna diferencijacija tijekom razvoja biljnih organa, leader: Vera Cesar (founded by MZOS, 2007.-2013. )

Posttraumatski stresni poremećaj djece ratnh veterana: kauzalni model
leader: doc.dr.sc. Ž. Vukšić-Mihaljević (founded by MZOS, 2001-2006)

Parameter identification problem in mathematical models
leader: prof.dr.sc. R. Scitovski (founded by MZOS, 1996-2000)

Teorijske i institucionalne pretpostavke poduzetničke ekonomije
leader: prof.dr.sc. S. Singer (1991.-1996.)

Theory of probability and mathematical statistics
leader: prof.dr.sc. N. Sarapa (1991-1996)

Zakon vrijednosti u funkciji upravljanja razvojem
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


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):  Četvrtkom (Thu) 12:00h od 1.9. 2019. do 10. 7. 2020. te od 31. 8.2020. nadalje. Konzultacije su moguće i po dogovoru.



Aktualna nastava:

Multivarijatna analiza (Multivariate Analysis)

Statistika (Statistics)

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

Vjerojatnost i statistika (Probability and Statistics), Faculty of Civil Engineering, University of Osijek 

Statistika (Statistics), FOOZOS, Undergraduate University Studies of Kinesiology

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

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

Primijenjena multivarijatna statistika (Građevinski 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:

  1. Monte Carlo metode
  2. Bayesovsko statističko zaključivanje
  3. Linearna regresija s hetroskedastičnim greškama
  4. Linerani model simultanih jedndžbi
  5. Steinov identitet i primjene 
  6. Teorija uzorkovanja: Dizajn eksperimenta 
  7. Analiza varijance u linearnom modelu 
  8. Kanoničke varijable 
  9. Distribucija produkta dvije nezavisne normalne slučajne varijable
  10. Moguće su i druge teme u dogovoru sa zainteresiranim studentom

Prijedlog tema završnih radova na Odjelu za matematiku:

  1. Jednostavno slučajno uzorkovanje
  2. Stratificirano slučajno uzorkovanje 
  3. Simuliranje podataka iz zadane distribucije
  4. Korisne metode opisa skupa podataka
  5. Uvjetne distribucije 



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:

Analiza vremenskih nizova (Time Series Analysis)

Statistički praktikum (Stat Labs)

Vjerojatnost (Probability)

Slučajni procesi (Random Processes)

Metodika nastave matematike 1

Metodika nastave matematike 2


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) 

Vjerojatnost i statisktika (Građevinski fakultet Osijek)




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