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 language | English |
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Pages (from-to) | 294-308 |
Number of pages | 15 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 52 |
Issue number | 2 |
DOIs | |
State | Published - 2023 |
Scopus Subject Areas
- Statistics and Probability
Keywords
- Binomial distribution
- binomial experiment
- q-analog
- quantum binomial theorem