The discrete q-Gaussian distribution Nq(μ, σ<SUP>2</SUP>): Properties and parameters estimation

作     者：Ben Mrad, Oumaima Masmoudi, Afif Slaoui, Yousri 

作者机构：Univ Sfax Lab Probabil & Stat Sfax Tunisia Univ Poitiers Lab Math & Applicat Poitiers France 

出 版 物：《PHYSICS LETTERS A》 (Phys Lett Sect A Gen At Solid State Phys)

年 卷 期：2024年第493卷

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：We would like to thank the Editor of Physics Letters A  Prof. Amita Das  and the reviewers for their helpful comments  which helped us to focus on improving the original version of the paper 

主　　题：q-calculus q-distribution q-Gaussian Finite mixture Parametric estimation EM algorithm 

摘      要：We introduce a new discrete distribution, called the centered reduced discrete q-Gaussian N-q(0,1). This distribution connects classical Gaussian, discrete Uniform, and quantum q-Gaussian distributions. In this paper, we extend N-q(0,1) to N-q(mu,sigma(2)), overcoming a limitation of some q-distributions like Diaz and Pariguan s q-Gaussian. Notably, N-q(0,1) has distinct shapes and parameters from the classical counterpart, providing additional flexible modeling approach. Results show the suggested discrete q-Gaussian as a useful alternative to the classical Gaussian for modeling data with hollow values or heavy-tailed tails. We explore properties of N-q(mu,sigma(2)) and apply moments and maximum likelihood methods to estimate its parameters. Our analysis yields a key result on the concavity of the likelihood function, enabling efficient optimization algorithms for parameters estimation. Furthermore, we investigate a finite mixture of discrete q-Gaussians and apply the EM algorithm for parameters estimation. Finally, we conduct a simulation study to evaluate the model and estimation methods.