A refinement of the binomial distribution using the quantum binomial theorem

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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 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.

Original languageEnglish
Pages (from-to)294-308
Number of pages15
JournalCommunications in Statistics - Theory and Methods
Volume52
Issue number2
DOIs
StatePublished - 2023

Scopus Subject Areas

  • Statistics and Probability

Keywords

  • Binomial distribution
  • binomial experiment
  • q-analog
  • quantum binomial theorem

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