
Home Departments Theoretical Methods Department Projects Discrete and continuous probabilistic models and their applications
Discrete and continuous probabilistic models and their applications 
Project of the Scientific Grant Agency VEGA 2/0047/15
Duration of the project: 01/2015  12/2017
Principal investigator: Prof. RNDr. Gejza Wimmer, DrSc. (Mathematical Institute SAS)
Principal investigator (IMS SAS): Doc. RNDr. Viktor Witkovský, CSc.
The project examines properties of discrete and continuous distributions, focusing on the following three objectives: (i) theoretical analysis of properties of discrete and continuous distributions; investigation of links between the probability distributions; creation of distribution families; development of new algorithms for random number generators for nonstandard discrete and continuous distributions; (ii) development of a pilot version of R toolbox for statistical goodnessoffit testing for selected discrete and continuous distributions; creating a pilot version of the "Internet Encyclopedia" of discrete and continuous distributions; (iii) applications of discrete and continuous distributions to mathematical modeling in metrology, linguistics, insurance and demographics.
In 2015, we continued within the project in the elaboration of methods for numerical inversion of the characteristic functions to calculate the probability distribution of random variables that arises from the linear combination or convolution of independent random variables. We designed and implemented first version of algorithms to calculate numerically the inverse Fourier transform of the combined characteristic functions for different classes of symmetric distributions. In particular, we have considered the distribution of linear combinations of independent random variables with normal, student, uniform, triangular and arcsine distribution, which often occurs in the analysis of the uncertainty analysis of measurement results. The suggested procedures were applied also for analysis of the interlaboratory comparison studies.
Publications:

WITKOVSKÝ, V.  WIMMER, G.  ĎURIŠ, S.: On
statistical methods for common mean and reference confidence intervals
in interlaboratory comparisons for temperature. International Journal of
Thermophysics 36(8), 2015, 21502171 (DOI 10.1007/s1076501519170).

KÖNING, R.  WIMMER, G.  WITKOVSKÝ, V.: The
statistical uncertainty of the Heydemann correction: a practical limit
of optical quadrature homodyne interferometry. Measurement Science and
Technology 26(8), 2015, 084004 (12pp) doi:10.1088/09570233/26/8/084004.

JAKUBÍK, J.: Convex method for variable selection
in highdimensional linear mixed models. In: Nagy, S., editor
Proceedings of the 19th European Young Statisticians Meeting 2015
Prague, August 31  September 4, 2015, 6468. MATFYZPRESS, Publishing
House of the Faculty of Mathematics and Physics, Charles University in
Prague.

JAKUBÍK, J.: Convex method for variable selection
in highdimensional linear mixed models. In: Witkovský, V., Somorčík,
J., editors, PROBASTAT 2015  The seventh international conference on
Probability and Statistics. Abstracts. Smolenice Castle, Slovak
Republic, June 29  July 3, 2015, 2930. Poster.

WIMMER, G.  WITKOVSKÝ, V.  KÖNING, R.: An
algorithm for demodulation of correlated quadrature interferometer
signals. In: Maňka, J., Tyšler, M., Witkovský, V., Frollo, I., editors,
MEASUREMENT 2015, Proceedings of the 10th International Conference on
Measurement Smolenice, Slovakia, May 2528, 2015, 1720. Institute of
Measurement Science, Slovak Academy of Sciences, Bratislava.

WITKOVSKÝ, V.: Numerical inversion of a
characteristic function: An alternative tool to form the probability
distribution of output quantity in linear measurement models. In: Holub,
J., editor IMEKO XXI World Congress  Full Papers. Prague, Czech
Republic, August 30  September 4, 2015, 20982101. Czech Technical
University in Prague, Faculty of Electrical Engineering, Department of
Measurement.

WITKOVSKÝ, V.: On computing distribution of the
AndersonDarling and Cramérvon Mises statistics by numerical inversion
of their characteristic functions. In: Witkovský, V., Somorčík, J.,
editors, PROBASTAT 2015  The seventh international conference on
Probability and Statistics. Abstracts. Smolenice Castle, Slovak
Republic, June 29  July 3, 2015, 53. Poster.

WITKOVSKÝ, V.  WIMMER, G.: Exact statistical
inference by using FFT inversion of the characteristic function. In:
Fišerová, E., Hron, K., Talašová, J., editors, ODAM 2015  Olomoucian
Days of Applied Mathematics. Palacký University in Olomouc, Czech
Republic, January 2628, 2015, 89. Palacký University in Olomouc, Czech
Republic. Invited Lecture.


Staff of Department of Theoretical Methods 
 Rošťáková, Zuznana, Mgr.
 Jakubík, Jozef, Mgr.
 Bajla, Ivan, prof. RNDr. Ing. PhD.
 Chvosteková, Martina, Mgr.
 Bartošová, Katarína, Ing. PhD.
 Grendár, Marián, Mgr. PhD
 Hornišová, Klára, Mgr. PhD
 Krakovská, Anna, RNDr. CSc.
 Rosipal, Roman, Ing. Mgr. PhD
 Rublík, František, Doc. RNDr. CSc.
 Štolc, Svorad, Mgr. PhD
 Mezeiová, Kristína, Mgr. PhD.
 Teplan, Michal, Mgr. PhD
 Witkovský, Viktor, Doc. RNDr. CSc.

