Optimum Group Limits for Maximum Likelihood Estimation of the Exponentiated Fréchet Distribution Based on Grouped Data
A. A. Marwa *
Department of Mathematical Statistics, Institute of Statistical Studies and Research, Cairo University, Egypt.
Hegazy Zaher
Department of Mathematical Statistics, Institute of Statistical Studies and Research, Cairo University, Egypt.
E. A. Elsherpieny
Department of Mathematical Statistics, Institute of Statistical Studies and Research, Cairo University, Egypt.
*Author to whom correspondence should be addressed.
Abstract
In many situations, instead of a complete sample, data are available only in grouped form. In this situation the values of individual observations are not known, but the number of observations that fall in each group is only known. Here the model under consideration is the exponentiated Fréchet distribution. The aim of this paper is finding the MLE's for the parameters of the exponentiated Fréchet distribution based on grouped data. The asymptotic variance-covariance matrix has been derived and computed numerically. Optimal group limits in the case unequi-spaced groupings so as to have a maximum asymptotic relative efficiency are worked out.
Keywords: Maximum likelihood estimation, exponentiated fréchet distribution, grouped data, optimum grouping.