q-geometric and q-binomial distributions of order k

摘要

In this paper, we generalize geometric and binomial distributions of order k to q-geometric and q-binomial distributions of order k using Bernoulli trials with a geometrically varying success probability. In particular, we derive expressions for the probability mass functions of these distributions. For q=1, these distributions reduce to geometric and binomial distributions of order k which have been extensively studied in the literature.