Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 51 Sayı: 5, 1472 - 1483, 01.10.2022

Öz

Kaynakça

  • [1] N. Balakrishnan and A. Stepanov, On the Fisher information in record data, Statist. Probab. Lett. 76 (5), 537-545, 2006.
  • [2] P.K. Bhattacharya, Estimation of a probability density function and its derivatives, Sankhya A 29 (4), 373-382, 1967.
  • [3] J.F. Bercher, Some properties of generalized Fisher information in the context of nonextensive thermostatistics, Phys. A 392 (15), 3140-3154, 2013.
  • [4] S.G. Bobkov, Moments of the scores, IEEE Trans. Inf. Theory 65 (9), 5294-5301, 2019.
  • [5] T. Duong, M. Wand, J. Chacon and A. Gramacki, Package “ks”, R package version: 1.13.5, 2022.
  • [6] R.A. Fisher, Tests of significance in harmonic analysis, Proc. R. Soc. A 125 (796), 54-59, 1929.
  • [7] S. Golomb, The information generating function of a probability distribution (corresp.), IEEE Trans. Inf. Theory 12 (1), 75-77, 1966.
  • [8] S. Guiasu and C. Reischer, The relative information generating function, Inform. Sci. 35 (3), 235-241, 1985.
  • [9] O. Kharazmi and N. Balakrishnan, Jensen-information generating function and its connections to some well-known information measures, Statist. Probab. Lett. 170, 1-10, 2021.
  • [10] F. Nielsen and R. Nock, On the chi square and higher-order chi distances for approximating f-divergences, IEEE Signal Process. Lett. 21 (1), 10-13, 2014.
  • [11] T. Papaioannou, K. Ferentinos and C. Tsairidis, Some information theoretic ideas useful in statistical inference, Methodol. Comput. Appl. Probab. 9 (2), 307-323, 2007.
  • [12] G. Pau, F. Fuchs, O. Sklyar, M. Boutros and W. Huber, EBImage-an R package for image processing with applications to cellular phenotypes, Bioinformatics 26 (7), 979-981, 2010.
  • [13] P. Sánchez-Moreno, A. Zarzo and J.S. Dehesa, Jensen divergence based on Fisher’s information, J. Phys. A Math. 45 (12), 125305, 2012.
  • [14] C.E. Shannon, A mathematical theory of communication, Bell Labs Tech. J. 27 (3), 379-423, 1948.
  • [15] P. Zegers, Fisher information properties, Entropy 17 (7), 4918-4939, 2015.

Generating function for generalized Fisher information measure and its application to finite mixture models

Yıl 2022, Cilt: 51 Sayı: 5, 1472 - 1483, 01.10.2022

Öz

In this work, we consider generating function for generalized Fisher information measure and use it to develop some results for this measure. Next, we study generalized Fisher information for the mixing parameter vector of a finite mixture density function and develop some results for this model. Further, we propose a Jensen-type divergence measure, namely, Jensen-generalized Fisher information (JGFI), and establish some properties for this measure and its generating function. Finally, for illustrative purposes, we examine a real example from image processing and provide some numerical results in terms of JGFI measure. 

Kaynakça

  • [1] N. Balakrishnan and A. Stepanov, On the Fisher information in record data, Statist. Probab. Lett. 76 (5), 537-545, 2006.
  • [2] P.K. Bhattacharya, Estimation of a probability density function and its derivatives, Sankhya A 29 (4), 373-382, 1967.
  • [3] J.F. Bercher, Some properties of generalized Fisher information in the context of nonextensive thermostatistics, Phys. A 392 (15), 3140-3154, 2013.
  • [4] S.G. Bobkov, Moments of the scores, IEEE Trans. Inf. Theory 65 (9), 5294-5301, 2019.
  • [5] T. Duong, M. Wand, J. Chacon and A. Gramacki, Package “ks”, R package version: 1.13.5, 2022.
  • [6] R.A. Fisher, Tests of significance in harmonic analysis, Proc. R. Soc. A 125 (796), 54-59, 1929.
  • [7] S. Golomb, The information generating function of a probability distribution (corresp.), IEEE Trans. Inf. Theory 12 (1), 75-77, 1966.
  • [8] S. Guiasu and C. Reischer, The relative information generating function, Inform. Sci. 35 (3), 235-241, 1985.
  • [9] O. Kharazmi and N. Balakrishnan, Jensen-information generating function and its connections to some well-known information measures, Statist. Probab. Lett. 170, 1-10, 2021.
  • [10] F. Nielsen and R. Nock, On the chi square and higher-order chi distances for approximating f-divergences, IEEE Signal Process. Lett. 21 (1), 10-13, 2014.
  • [11] T. Papaioannou, K. Ferentinos and C. Tsairidis, Some information theoretic ideas useful in statistical inference, Methodol. Comput. Appl. Probab. 9 (2), 307-323, 2007.
  • [12] G. Pau, F. Fuchs, O. Sklyar, M. Boutros and W. Huber, EBImage-an R package for image processing with applications to cellular phenotypes, Bioinformatics 26 (7), 979-981, 2010.
  • [13] P. Sánchez-Moreno, A. Zarzo and J.S. Dehesa, Jensen divergence based on Fisher’s information, J. Phys. A Math. 45 (12), 125305, 2012.
  • [14] C.E. Shannon, A mathematical theory of communication, Bell Labs Tech. J. 27 (3), 379-423, 1948.
  • [15] P. Zegers, Fisher information properties, Entropy 17 (7), 4918-4939, 2015.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm İstatistik
Yazarlar

Omid Kharazmi 0000-0003-4176-9708

Narayanaswamy Balakrishnan 0000-0001-5842-8892

Yayımlanma Tarihi 1 Ekim 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 5

Kaynak Göster

APA Kharazmi, O., & Balakrishnan, N. (2022). Generating function for generalized Fisher information measure and its application to finite mixture models. Hacettepe Journal of Mathematics and Statistics, 51(5), 1472-1483. https://doi.org/10.15672/hujms.1094273
AMA Kharazmi O, Balakrishnan N. Generating function for generalized Fisher information measure and its application to finite mixture models. Hacettepe Journal of Mathematics and Statistics. Ekim 2022;51(5):1472-1483. doi:10.15672/hujms.1094273
Chicago Kharazmi, Omid, ve Narayanaswamy Balakrishnan. “Generating Function for Generalized Fisher Information Measure and Its Application to Finite Mixture Models”. Hacettepe Journal of Mathematics and Statistics 51, sy. 5 (Ekim 2022): 1472-83. https://doi.org/10.15672/hujms.1094273.
EndNote Kharazmi O, Balakrishnan N (01 Ekim 2022) Generating function for generalized Fisher information measure and its application to finite mixture models. Hacettepe Journal of Mathematics and Statistics 51 5 1472–1483.
IEEE O. Kharazmi ve N. Balakrishnan, “Generating function for generalized Fisher information measure and its application to finite mixture models”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 5, ss. 1472–1483, 2022, doi: 10.15672/hujms.1094273.
ISNAD Kharazmi, Omid - Balakrishnan, Narayanaswamy. “Generating Function for Generalized Fisher Information Measure and Its Application to Finite Mixture Models”. Hacettepe Journal of Mathematics and Statistics 51/5 (Ekim 2022), 1472-1483. https://doi.org/10.15672/hujms.1094273.
JAMA Kharazmi O, Balakrishnan N. Generating function for generalized Fisher information measure and its application to finite mixture models. Hacettepe Journal of Mathematics and Statistics. 2022;51:1472–1483.
MLA Kharazmi, Omid ve Narayanaswamy Balakrishnan. “Generating Function for Generalized Fisher Information Measure and Its Application to Finite Mixture Models”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 5, 2022, ss. 1472-83, doi:10.15672/hujms.1094273.
Vancouver Kharazmi O, Balakrishnan N. Generating function for generalized Fisher information measure and its application to finite mixture models. Hacettepe Journal of Mathematics and Statistics. 2022;51(5):1472-83.