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. S. Hamedović, M. Benšić, K. Sabo, P. Taler, Estimating the size of an object captured with error, Central European Journal of Operations Research (2017), prihvaćen za objavljivanje
    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.
  2. 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
  3. J. Flam, D. Gugić, M. Benšić, S. Tomić, J. Rajc, High tumor stroma proportion is a worse prognostic factor colorectal cancer , ACTA CLINICA CROATICA 56 (2017)
  4. 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 (2017), prihvaćen za objavljivanje
    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.
  5. 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.
  6. 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.
  7. 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
  8. J. Milić, A. Kvolik, A. Babić Čikeš, I. Labak, M. Benšić, V. Ilakovac, M. Ništ, L. Zibar, M. Heffer-Lauc, Are There Differences in Students’ School Success, Biorhythm, and Daytime Sleepiness Depending on Their School Starting Times?, Collegium antropologicum 38/3 (2014), 889-893
  9. M. Benšić, Fitting distribution to data by a generalized nonlinear least squares method, Communications in statistics-simulation and computation 43/4 (2014), 687-705
    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.
  10. 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


  • 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


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):  Četvrtak (Thu) 11:00h. 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 


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)


Prijedlog tema diplomskih radova na Odjelu za matematiku:

  1. Steinov identitet i primjene 
  2. Teorija uzorkovanja: Dizajn eksperimenta 
  3. Analiza varijance u linearnom modelu 
  4. Kanoničke varijable 
  5. Distribucija produkta dvije nezavisne normalne slučajne varijable
  6. Moguće su i druge teme u dogovoru sa zainteresiranim studentom



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)