A Study on Estimating the Parameter of the Truncated Geometric Distribution

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.

Keywords:

• Existence of estimator
• Maximum likelihood estimation
• Method of moments estimator
• Truncated geometric distribution

Acknowledgments

The authors would like to acknowledge the comments and suggestions from the Editor, an Associate Editor, and the two anonymous reviewers’ inputs have substantially improved the quality of the article.

Additional information

Funding

Dr. Park’s work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (NRF-2017R1A2B4004169).