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 non-standard discrete and continuous distributions; (ii) development of a pilot version of R toolbox for statistical goodness-of-fit 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 inter-laboratory comparison studies.

Publications: 

1. 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, 2150-2171 (DOI 10.1007/s10765-015-1917-0).
2. 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:10.1088/0957-0233/26/8/084004.
3. JAKUBÍK, J.: Convex method for variable selection in high-dimensional linear mixed models. In: Nagy, S., editor Proceedings of the 19th European Young Statisticians Meeting 2015 Prague, August 31 - September 4, 2015, 64-68. MATFYZPRESS, Publishing House of the Faculty of Mathematics and Physics, Charles University in Prague.
4. JAKUBÍK, J.: Convex method for variable selection in high-dimensional 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, 29-30. Poster.
5. 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 25-28, 2015, 17-20. Institute of Measurement Science, Slovak Academy of Sciences, Bratislava.
6. 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, 2098-2101. Czech Technical University in Prague, Faculty of Electrical Engineering, Department of Measurement.
7. WITKOVSKÝ, V.: On computing distribution of the Anderson-Darling and Cramér-von 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.
8. 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 26-28, 2015, 89. Palacký University in Olomouc, Czech Republic. Invited Lecture.