Maximum-Likelihood Parameter Estimation of a Generalized Gumbel Distribution

摘要

A microcomputer-based algorithm for estimation of the three parameters of a generalized Gumbel (extreme value type I) distribution class is presented. The parameters are shift, scale, and shape. The classical Gumbel distribution results if the shape parameter is equal to unity. Three-parameter as well as two-parameter (shape equal to unity) estimation can be performed for given histogram data. Parameter estimation is accomplished by means of the maximum-likelihood principle. The derivative equations which result from the associated logarithmic likelihood function are used. A more comprehensive presentation of generalized Gumbel distribution estimation which also allows treatment of population data and which includes moment estimates and maximum-likelihood estimates by direct optimization of the logarithmic likelihood function will be presented elsewhere. (Author).