González, Eduardo Gutiérrez; Panteleeva, Olga Vladimirovna; Córdoba Lobo, Víctor Manuel Maximum likelihood estimators for the parameters of a distribution extended log-loc-scale class. (English) Zbl 1285.62015 Far East J. Theor. Stat. 40, No. 2, 127-143 (2012). 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 Keywords:generalized log-gamma distribution; shape parameter; location-scale distribution PDFBibTeX XMLCite \textit{E. G. González} et al., Far East J. Theor. Stat. 40, No. 2, 127--143 (2012; Zbl 1285.62015) Full Text: Link