A Study on Estimating the Parameter of the Truncated Geometric Distribution

Chanseok Park, Kun Gou and Min Wang

The American Statistician, 2022, vol. 76, issue 3, 257-261

Abstract: We consider the truncated geometric distribution and analyze the condition under which a nontrivial maximum likelihood (ML) estimator of the parameter p exists. Additionally, the uniqueness criterion of such an ML estimator is also investigated. Our results indicate that in order to ensure the existence of a nontrivial ML estimator, the sample mean should be smaller than the midpoint of the two boundary positions. Without such a condition, the ML estimator will only exist trivially at p = 0. Finally, we demonstrate that the same condition is also required for the existence of the method of moments estimator. Our results lead to a rigorous understanding of the two estimators and aid in the interpretation of experimental designs that incorporate the truncated geometric distribution.

Date: 2022
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DOI: 10.1080/00031305.2022.2034666

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