A refinement of the binomial distribution using the quantum binomial theorem

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. Her...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2023-01, Vol.52 (2), p.294-308
Main Author: Sills, Andrew V.
Format: Article
Language:English
Subjects:
Analogs
Binomial distribution
binomial experiment
Binomial theorem
Hypergeometric functions
Mathematical analysis
Primary 60C05
secondary 05A30, 05A10
q-analog
quantum binomial theorem
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Summary: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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2021.1912768