A Surprising MLE for Interval-Censored Binomial Data

Jesse Frey Jesse Frey is Assistant Professor, and Osvaldo Marrero is Professor, Department of Mathematical Sciences, Villanova University, Villanova, PA 19085 (Email for correspondence: . The authors thank H. N. Nagaraja, editor Peter Westfall, and an anonymous referee for valuable suggestions that have improved the article.

Osvaldo Marrero Jesse Frey is Assistant Professor, and Osvaldo Marrero is Professor, Department of Mathematical Sciences, Villanova University, Villanova, PA 19085 (Email for correspondence: . The authors thank H. N. Nagaraja, editor Peter Westfall, and an anonymous referee for valuable suggestions that have improved the article.

Abstract

We derive the maximum likelihood estimator of the binomial success probability when the number of trials is known, but the number of successes is only known to fall in some interval. This estimator has a surprisingly simple form. Specifically, the maximum likelihood estimate of the log odds of success is the mean of the maximum likelihood estimates of the log odds of success that are obtained by letting the number of successes take on each integer value in the interval. An application is suggested.

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A Surprising MLE for Interval-Censored Binomial Data

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A Surprising MLE for Interval-Censored Binomial Data

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