PARAMETER ESTIMATION OF THE SHAPE PARAMETER OF THE GAMMA DISTRIBUTION FREE FROM LOCATION AND SCALE INFORMATION

• Published in: Advanced Reliability Modeling II pp. 626 - 633
• Main Authors: NAGATSUKA, HIDEKI, YAMAMOTO, HISASHI, KAMAKURA, TOSHINARI
• Format: Book Chapter
• Language: English; Japanese
• Published: WORLD SCIENTIFIC 01.07.2006
• Subjects: VII. Statistical Analysis and Reliability Modeling; Gamma distribution; Maximum likelihood estimator; Threshold parameter; Location and scale parameter free; Order statistics; Method of moments
• ISBN: 9814478121; 9789812773760; 9812567585; 9789814478120; 9812773762; 9789812567581
• DOI: 10.1142/9789812773760_0075

The gamma distribution, having location (threshold), scale and shape parameters, is used as a model for distributions of life spans, reaction time, and for other types of non-symmetrical data. It has been said that the inference for the three-parameter gamma distribution is difficult because of nonregularity in maximum likelihood estimation although numerous papers have appeared over the years. On the other hand, the methodology for inference for the two-parameter gamma distribution have been established over the years. It is usual to avoid fitting the three-parameter gamma distribution and to fit the two-parameter gamma distribution to data in practice. In this article, we propose a new method of estimation of the shape parameter of the gamma distribution based on the data transformation free from location and scale parameters. The method is easily implemented with the aid of table or graph. A simulation study shows that the proposed estimator performs better than the maximum likelihood estimator of the shape parameter of the two-parameter gamma distribution when the threshold is existent even though that is close to zero.