On multivariate discrete q-Distributions-A multivariate q-Cauchy’s formula

Abstract

The main objective of this work is to introduce multivariate discrete q-distributions. We consider the Heine process $\{X_q(t),t>0\},0<q<1,$ where the random variable $X_q(t),$ for every $t>0,$ represents the number of events during a time interval $(0,t]$ and we reveal a multivariate discrete q-distribution related to the absorption distribution. By this multivariate discrete q-distribution, we introduce a multivariate absorption distribution and a multivariate q-hypergeometric distribution. Also, we deduce by a probabilistic proof a multivariate q-Cauchy’s formula and then a multivariate q-Vandermonde’s formula.

Keywords:

• Heine process
• absorption distribution
• q-hypergeometric distribution
• multivariate absorption distribution
• multivariate q-hypergeometric distribution
• multivariate q-Cauchy’s and q-Vandermonde’s formulae

MATHEMATICS SUBJECT CLASSIFICATION:

• 60C05
• 05A30

Acknowledgment

The author would like to thank the anonymous referees for their helpful and insightful comments and suggestions.

Disclosure statement

The author declares no conflict of interest.