Exact Sample Size Methods for Estimating Parameters of Discrete Distributions

TL;DR

This paper presents a method for precisely calculating the minimum sample size needed to estimate the expectation of a discrete, integer-valued random variable, simplifying the process by reducing infinite evaluations to a finite set.

Contribution

It introduces an exact approach for sample size determination for discrete distributions, leveraging properties of coverage probability to reduce computational complexity.

Findings

Exact sample size computation is feasible under certain assumptions.

Coverage probability minimums occur at a finite set of parameter values.

Method simplifies and improves precision of sample size estimation.

Abstract

In this paper, we develop an approach for the exact determination of the minimum sample size for estimating the parameter of an integer-valued random variable, which is parameterized by its expectation. Under some continuity and unimodal property assumptions, the exact computation is accomplished by reducing infinite many evaluations of coverage probability to finite many evaluations. Such a reduction is based on our discovery that the minimum of coverage probability with respect to the parameter bounded in an interval is attained at a discrete set of finite many values.