Two-Stage and Sequential Unbiased Estimation of N in Binomial Trials, when the Probability of Success p is Unknown

TL;DR

This paper introduces two-stage and sequential methods for estimating the unknown number of trials N in a binomial distribution when the success probability p is unknown, utilizing additional negative-binomial data.

Contribution

The paper presents novel two-stage and sequential estimation procedures that incorporate negative-binomial samples to estimate N without prior knowledge of p.

Findings

Effective estimation of N using the proposed methods.

Procedures work with unknown success probability p.

Enhanced accuracy with additional negative-binomial data.

Abstract

We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative-binomial experiment having the same p.