Two-stage and sequential unbiased estimation of N in binomial trials, when the probability of success p is unknown

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.

KEYWORDS:

• Sequential sampling
• two-stage sampling
• unbiased estimation

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62L05
• 62L12

ACKNOWLEDGEMENT

We thank the Editor, Associate Editor, and three referees for the insightful and helpful comments that led to improvements in the article.

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

The research of YM was supported by Grant No. 2020063 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel.