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Maximum likelihood estimators for the parameters of a distribution extended log-loc-scale class. (English) Zbl 1285.62015

Summary: An extension of the class to log-scale distributions that has a third shape parameter is proposed. The extended class consists of pairs of random variables related to a logarithmic or exponential transformation. A method for calculating maximum likelihood estimates of the three parameters in each distribution is proposed. The method is applied to a pair of generalized gamma and generalized log-gamma distributions, both with three parameters. The shape parameter shows that the maximum likelihood estimator is asymptotically unbiased and consistent in the mean square error.

MSC:

62E10 Characterization and structure theory of statistical distributions
62F10 Point estimation
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