Modified Moment Estimation for the Three-Parameter Gamma Distribution

Abstract

A modification of moment estimators for parameters of the three-parameter gamma distribution, in which the third moment is replaced with a function of the first order statistic is presented in this article. Calculations are made easy with the aid of accompanying charts and tables. The modified moment estimators enjoy advantages over the traditional moment and maximum likelihood estimators with respect to both estimate bias and variance. Unlike the maximum likelihood estimators, which break down in the presence of a high degree of skewness and which often lead to computational difficulties when samples are small, the modified moment estimators exist and are easy to calculate for all possible parameter values even when samples are small. Two illustrative examples are included. Also included are results of a simulation study in which sampling behavior of the modified moment estimators is compared with that of moment and maximum likelihood estimators.

• Reliability Analysis
• Life Span Analysis
• Parameter Estimation
• Skewed Distributions
• Gamma Distribution
• Moment Estimations

Additional information

Notes on contributors

A. Clifford Cohen

Dr. Cohen is an Emeritus Professor in the Department of Statistics. He is a Founding Member and a Fellow of ASQC.

Betty Jones Whitten

Dr. Whitten is an Associate Professor in the Department of Management Sciences in the College of Business Administration.