A SEQUENCE OF DISTRIBUTIONS WITH A FINITE SET OF VALUES ASYMPTOTICALLY EQUAL TO THE POISSON DISTRIBUTION

UDC 519.213: 51-77
DOI: 10.36871/2618-9976.2023.04.005

Authors

Sergei Ya. Krivolapov,
Candidate of Physicomathematical Science, Assistant Professor Department of Mathematics, Financial University under Govenment of Russian Federation, Moscow, Russia

Abstract

A sequence of random variables X(λ,n) with parameters 0 < λ≤1, n∈N is investigated. For n→∞ X(λ,n) converges in distribution to a random variable Pois(λ) obeying Poisson's law with the parameter λ. At a fixed value n all moments of the distribution of a random variable X(λ,n) of order k≤n coincide with the moments of the distribution of Pois(λ). For the value of the parameter λ=1, the random variable X(1,n) coincides with the random variable equal to the number of «fixed» points in case of random permutations of the set of elements of power n.

Keywords

Finite set permutations, Distribution moments, Bell numbers, Poisson distribution