Estimating the Reciprocal of a Binomial Proportion

Jiajin Wei, Ping He*, Tiejun Tong*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


The binomial proportion is a classic parameter with many applications and has also been extensively studied in the literature. By contrast, the reciprocal of the binomial proportion, or the inverse proportion, is often overlooked, even though it also plays an important role in various fields. To estimate the inverse proportion, the maximum likelihood method fails to yield a valid estimate when there is no successful event in the Bernoulli trials. To overcome this zero-event problem, several methods have been introduced in the previous literature. Yet to the best of our knowledge, there is little work on a theoretical comparison of the existing estimators. In this paper, we first review some commonly used estimators for the inverse proportion, study their asymptotic properties, and then develop a new estimator that aims to eliminate the estimation bias. We further conduct Monte Carlo simulations to compare the finite sample performance of the existing and new estimators, and also apply them to handle the zero-event problem in a meta-analysis of COVID-19 data for assessing the relative risks of physical distancing on the infection of coronavirus.
Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalInternational Statistical Review
Issue number1
Early online date20 Mar 2023
Publication statusPublished - Apr 2024

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • binomial proportion
  • inverse proportion
  • relative risk
  • shrinkage estimator
  • zero-event problem


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