q-probability: I. Basic discrete distributions

TL;DR

This paper introduces q-analogs for fundamental discrete probability distributions, expanding the mathematical framework and potential applications in probability theory.

Contribution

It proposes q-analogs for basic discrete distributions such as Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform distributions.

Findings

Defined q-analogs for key discrete distributions

Provides mathematical properties of the q-analogs

Lays groundwork for further research in q-distributions

Abstract

For basic discrete probability distributions, $-$ Bernoulli, Pascal, Poisson, hypergeometric, contagious, and uniform, $-$ $q$-analogs are proposed.