On a generalized q-binomial distribution and new q-multinomial distribution

The current study primarily introduces a novel q-multinomial distribution, derived from a stochastic model involving a sequence of q-multinoulli trials. This distribution is defined based on strict and specific rules or assumptions regarding the probabilities of outcome. It provides fresh perspectives and q-tools in its development methodology, which differ significantly from those discussed in existing literature, and it extends the concept of the q-binomial distribution. Other possible uses for an expanded range of q-discrete distributions, associated with the q-binomial distribution and offering a wider scope than those previously examined in existing literature, have also been addressed.