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Gamma distribution shape parameter bias
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1980
[PDF-66.12 MB]
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Description:The generalized gamma distribution has three parameters, the origin, the scale, and the shape. As a model, it serves to approximate univariate distributions in many disciplines. To be an acceptably accurate model, the model parameters estimates should contain no bias or should contain as little a bias as possible. To be a more useful model, the model should show the confidence in the fit it provides to a data set.
Rarely is the bias removed in actual practice. Only recently have procedures to remove bias been developed. The two most widely used estimators, the moments and the maximum likelihood estimators, exhibit a bias which is a function of the sample size and of the shape parameters. The Thom estimator, which is an approximation to the maximum likelihood estimator, should and does exhibit the same bias. The origin is assumed to be fixed. Only two parameters are thus involved, the shape and the scale.
A recent paper by the authors treats the subject of this paper for shape parameters equal to or greater than one. This paper re-examines the region from a shape parameter of 5 down to 1 and extends the removal of bias procedures down to shape parameters of two-hundredths, 0.02, with a sample size 2 or greater.
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Rights Information:Public domain
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