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arXiv · 2009.12641

A refinement of the binomial distribution using the quantum binomial theorem

Andrew V. Sills
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Abstract

$q$-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 refinement of the binomial distribution by way of the quantum binomial theorem (also known as the the noncommutative $q$-binomial theorem), where the $q$ is a formal variable in which information related to the sequence of successes and failures in the underlying binomial experiment is encoded in its exponent.

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BibTeXRIS

Andrew V. Sills. 2020-09-26. A refinement of the binomial distribution using the quantum binomial theorem. https://doi.org/10.1080/03610926.2021.1912768

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