Beta distribution and associated Stirling numbers of the second kind
Jakub Gismatullin, Patrick Tardivel
TL;DR
This paper derives a formula linking associated Stirling numbers of the second kind to moments of beta-distributed variables and uses probabilistic methods to establish bounds for these numbers.
Contribution
It introduces a novel formula connecting Stirling numbers to beta distribution moments and provides new probabilistic bounds for these numbers.
Findings
Derived a formula for associated Stirling numbers using beta distribution moments
Established probabilistic lower and upper bounds for these numbers
Connected combinatorial numbers with probabilistic methods
Abstract
This article gives a formula for associated Stirling numbers of the second kind based on the moment of a sum of independent random variables having a beta distribution. From this formula we deduce, using probabilistic approaches, lower and upper bounds for these numbers.
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