Integrals of incomplete beta functions, with applications to order statistics, random walks and string enumeration

@article{Connor2022IntegralsOI,
  title={Integrals of incomplete beta functions, with applications to order statistics, random walks and string enumeration},
  author={Stephen B. Connor and Christopher J. Fewster},
  journal={Brazilian Journal of Probability and Statistics},
  year={2022}
}
Abstract. We study the probability that one beta-distributed random variable exceeds the maximum of two others, allowing all three to have general parameters. This amounts to studying Euler transforms of products of two incomplete beta functions. We provide a closed form for the general problem in terms of Kampé de Fériet functions and a variety of simpler closed forms in special cases. The results are applied to derive the moments of the maximum of two independent beta-distributed random… 

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