Finite-sample frequency distributions originating from an equiprobability distribution

TL;DR

This paper investigates the expected rank-ordered frequency distribution resulting from an ensemble of M events drawn from an equiprobability distribution over N outcomes.

Contribution

It derives the finite-sample frequency distribution for an ensemble drawn from a uniform probability distribution, providing analytical insights into its expected behavior.

Findings

Derived the expected rank-ordered frequency distribution for finite samples.

Provided analytical formulas for the distribution based on sample size and number of outcomes.

Enhanced understanding of sampling variability from uniform distributions.

Abstract

Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the expected corresponding rank ordered frequency distribution f(i), i=1..N, if an ensemble of M events is drawn?