A q-analog of the binomial distribution

Andrew V. Sills

Published 2020-09-26Version 1

$q$-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 continuous distributions have been introduced over the years. Here I propose a $q$-analog of a discrete distribution: the binomial distribution.