A refinement of the binomial distribution using the quantum binomial theorem
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909308059385856 |
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| author | Sills, Andrew V. |
| author_facet | Sills, Andrew V. |
| contents | $q$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_12641 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A refinement of the binomial distribution using the quantum binomial theorem Sills, Andrew V. Probability Combinatorics Statistics Theory 60E05 $q$-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. |
| title | A refinement of the binomial distribution using the quantum binomial theorem |
| topic | Probability Combinatorics Statistics Theory 60E05 |
| url | https://arxiv.org/abs/2009.12641 |