On characterizing the gamma and the beta $q$-distributions
Bull. Korean Math. Soc. 2018 Vol. 55, No. 5, 1563-1575
Published online September 30, 2018
Imen Boutouria, Imed Bouzida, Afif Masmoudi
Sfax University, Sfax University, Sfax University
Abstract : In this paper, our central focus is upon gamma and beta $q$-distributions from a probabilistic viewpoint. The gamma and the beta $q$-distributions are characterized by investing the nature of the joint $q$-probability density function through the $q$-independence property and the $q$-Laplace transform.
Keywords : $q$-calculus, $q$-Laplace transform, gamma $q$-distribution, beta $q$-distribution
MSC numbers : 60A05, 33E20
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