Dimorphic properties of Bernoulli random variable
taekyun Kim, Dae san kim, Hyunseok Lee, Seongho Park
TL;DR
This paper investigates a dimorphic property of Bernoulli sums with different distributions and derives new expressions involving Stirling numbers related to these sums.
Contribution
It introduces a novel dimorphic property for Bernoulli sums and connects it with new identities involving degenerate Stirling and Stirling numbers.
Findings
Identifies a dimorphic property in Bernoulli sums
Derives expressions linking Bernoulli sums with Stirling numbers
Provides new identities involving degenerate Stirling numbers
Abstract
The aim of this paper is to study a dimorphic property associated with two different sums of identically independent Bernoulli random variables having two different families of probability mass functions. In addition, we give two expressions on sums of products of degenerate Stirling numbers of the second kind and Stirling numbers of the first kind connected with those two different sums of identically independent Bernoulli random variables.
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Taxonomy
TopicsBayesian Methods and Mixture Models · Statistical Distribution Estimation and Applications · Stochastic processes and financial applications