A q-analog of the binomial distribution

09/26/2020

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by   Andrew V. Sills, et al.

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q-analogs of special functions, including hypergeometric functions, play a central role in mathematics and have numerous applications in physics. In the theory of probability, q-analogs of various probability distributions have been introduced over the years, including the binomial distribution. Here, I propose a new q-analog of the binomial distribution inspired by the classical noncommutative q-binomial theorem, where the q is a formal variable in which information related to the underlying binomial experiment is encoded in its exponent.