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The binomial distribution maximises entropy among sums of negatively related indicators with fixed mean and support

  • Fraser Daly
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Abstract

We show that the binomial distribution supported on {0,1,…,n} and with mean np for some 0<p<1 maximises entropy within the class of sums of negatively related indicator random variables with this mean and support. Our results generalise the main result of Yu (2008), who showed that this binomial distribution maximises entropy within the smaller class of ultra-log-concave random variables of order n. Our proof makes use of a Markov chain construction of Yu (2008), together with a stochastic ordering argument.

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Cite

BibTeXRIS
BibTeX
@misc{daly2026binomial,
  title = {{The binomial distribution maximises entropy among sums of negatively related indicators with fixed mean and support}},
  author = {Fraser Daly},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26543},
  eprint = {2610.26543},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26543},
}
RIS
TY  - UNPB
TI  - The binomial distribution maximises entropy among sums of negatively related indicators with fixed mean and support
AU  - Fraser Daly
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26543
UR  - https://arxiv.org/abs/2610.26543
AB  - We show that the binomial distribution supported on {0,1,…,n} and with mean np for some 0<p<1 maximises entropy within the class of sums of negatively related indicator random variables with this mean and support. Our results generalise the main result of Yu (2008), who showed that this binomial distribution maximises entropy within the smaller class of ultra-log-concave random variables of order n. Our proof makes use of a Markov chain construction of Yu (2008), together with a stochastic ordering argument.
ER  -