A Study on Estimating the Parameter of the Truncated Geometric Distribution. Issue 3 (3rd July 2022)

• Record Type: Journal Article
• Authors: Park, Chanseok; Gou, Kun; Wang, Min
• Is Part Of: American statistician. Volume 76:Issue 3(2022)
• Page Start: 257
• Page End: 261
• Publication Date: 2022-07-03
• Subjects: Existence of estimator -- Maximum likelihood estimation -- Method of moments estimator -- Truncated geometric distribution; Statistics -- Periodicals; 001.42205
• DOI: 10.1080/00031305.2022.2034666
• Languages: English
• ISSNs: 0003-1305

Abstract

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.