Kristian Sabo


ksabo web

Full Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia¸

Google Scholar Profile

phone: +385-31-224-827
fax: +385-31-224-801
email:  ksabo @
office:  18 (ground floor)


Research Interests

Applied and Numerical Mathematics (Curve Fitting, Parameter Estimation, Data Cluster Analysis) with applications in Agriculture, Economy, Chemistry, Politics, Electrical Engineering, Medicine, Food Industry, Mechanical Engineering.


PhD in Numerical Mathematics, Department of Mathematics, University of Zagreb, 2007
MSc in Mathematics, Department of Mathematics, University of Zagreb, 2003
BSc in Mathematics and Computer Science, Department of Mathematics, Croatia, 1999


Journal Publications

  1. A. Barron, M. Benšić, K. Sabo, A Note on Weighted Least Square Distribution Fitting and Full Standardization of the Empirical Distribution Function, TEST (2018), prihvaćen za objavljivanje
    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.
  2. 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.
  3. S. Majstorović, K. Sabo, J. Jung, M. Klarić, Spectral methods for growth curve clustering, Central European Journal of Operations Research 26/3 (2018), 715-737
    The growth curve clustering problem is analyzed and its connec- tion with the spectral relaxation method is described. For a given set of growth curves and similarity function, a similarity matrix is defined, from which the corresponding similarity graph is constructed. It is shown that a nearly op- timal growth curve partition can be obtained from the eigendecomposition of a specific matrix associated with a similarity graph. The results are illus- trated and analyzed on the set of synthetically generated growth curves. One real-world problem is also given.
  4. R. Scitovski, M. Vinković, K. Sabo, A. Kozić, A research project ranking method based on independent reviews by using the principle of the distance to the perfectly assessed project, Croatian Operational Research Review 8 (2017), 429-442
    The paper discusses the problem of ranking research projects based on the assessment obtained from n ≥ 1 independent blinded reviewers. Each reviewer assesses several project features, and the total score is defined as the weighted arithmetic mean, where the weights of features are determined according to the well-known AHP method. In this way, it is possible to identify each project by a point in n-dimensional space. The ranking is performed on the basis of the distance of each project to the perfectly assessed project. Thereby the application of different metric functions is analyzed. We believe it is inappropriate to use a larger number of decimal places if two projects are almost equidistant (according to some distance function) to the perfectly assessed project. In that case, it would be more appropriate to give priority to the project that has received more uniform ratings. This can be achieved by combining different distance functions. The method is illustrated by several simple examples and applied by ranking internal research projects at Josip Juraj Strossmayer University of Osijek, Croatia.
  5. 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.


  • Scientifically branded Pork (Member of the scientific project entitled above. Project started on June 1, 2014. Principal investigator is professor Goran Kušec from Faculty of Agriculture in Osijek, University of Osijek. Project was supported by Croatian Science Foundation.)


Professional Activities

Editorial Board

Since 2012 member of the Editorial board of the Journal Osječki matematički list

2001-2012 Editor in Chief of the Journal Osječki matematički list



Committee Memberships
  •  Member of the Organize Committee of the 4th Croatian Congress of Mathematics, Osijek, 2008
  •  Member of the Organize Committee of the 15th International Conference on Operational Research, Croatian Operational Research Society, Osijek 2014



Journal of Computational and Applied Mathematics, Journal of Classification, Mathematical Communications,  International Journal of Applied and Mathematics and Computer Science, Croatian Operational Research Review, TEAM 2012 International Conference, Osječki matematički list


Service Activities

Since 2013 president of Osijek Mathematical Society

2001-2013 secretary of Osijek Mathematical Society


Selected Other Activities (in Croatian)


  • 2014., 2015.  Večer matematike – manifestacija popularizacije matematike u organizaciji Udruge matematičara Osijeku i Hrvatskog matematičkog društva -  Član Programskog i Organizacijskog odbora
  •  2013.-2016. Matematičke pripreme za učenike srednjih škola • Programski i Organizacijski koordinator
  • 2000.-2016. Zimska matematička škola za učenike srednjih škola  • Član Programskog i Organizacijskog odbora
  • 2000.-2016. Zimska matematička škola za učenike osnovnih škola  • Član Programskog i Organizacijskog odbora
  • 2006.-2016. Stručni kolokvij Udruge matematičara Osijek • Član Programskog i Organizacijskog odbora
  • travanj, 2014.  Geometrijska škola Stanko Bilinski, Našice:  Predavanje za nastavnike: „Funkcija udaljenosti i odgovarajuća geometrija“,  Radionica za učenike: “Neki optimizacijski problemi u geometriji“
  • travanj, 2014. Festival znanosti Sveučilišta Josipa Jurja Strossmayera u Osijeku  Predavanje: „Što su optimalne izborne (upravne) jedinice i kako ih odrediti“.  Član Programskog i Organizacijskog odbora
  • listopad, 2012. Stručni skup: Nastava matematike i izazovi moderne tehnologije u organizaciji Udruge Normala - Predavanje: „Zaglađivanje podataka: metode, pristupi i primjene“



Teaching (in Croatian)

Konzultacije: Srijeda  11:00 - 12:00

Teme zavšnih i diplomskih radova (pdf)


Zimski semestar 2017./2018.


Matematika I, Prehrambeno tehnološki fakultet

Primijenjena i Inženjerska matematika, Prehrambeno tehnološki fakultet



Ljetni semestar 2015./2016.

Grupiranje podataka: pristupi, metode i primjene,  ponedjeljak 13:00 - 17:00, RP2

Linearno programiranje, petak 8:00-12:00, RP1

Numerička analiza, srijeda 10:00-12:00, P24


Zimski semestar 2015./2016.

 Diferencijalni račun, utorak, 8:00 - 11:00, P 1

 Matematički praktikum, srijeda, 8:00-10:00


Ljetni semestar 2014./2015.

Grupiranje podataka: pristupi, metode i primjene,  ponedjeljak 13:00 - 17:00, RP2

Linearno programiranje, utorak 15:00-19:00, P3

Numerička analiza, srijeda 8:00-10:00, P24

Primjene diferencijalnog i integralnog računa II, srijeda 10:00-11:00, P2




  • Birthdate: November 23, 1975
  • Birthplace: Kula, Vojvodina, Serbia
  • Family: married with Marija, and have one daughter Paula


Udžbenik Linearno programiranje (pdf)


Uvodni sat (pptx)

Izvjesce procelnika 2017/2018 (pdf)