Asymptotic Properties of MLE's for Distributions Generated from an Exponential Distribution by a Generalized Log-Logistic Transformation

Abstract

ABSTRACT.  A generalized log-logistic (GLL) family of lifetime distributions is one in which any pair of distributions are related through a GLL transformation, for some (non-negative) value of the transformation parameter k (the odds function of the second distribution is the k-th power of the odds function of the first distribution).  We consider GLL families generated from an exponential distribution.  It is shown that the Maximum Likelihood Estimators (MLE’s) for the parameters of the generated, or composite, distribution have the properties of strong consistency and asymptotic normality and efficiency.  Data simulation is also found to support the condition of asymptotic efficiency.      Keywords Generalized log-logistic exponential distribution; asymptotic properties of MLE’s; simulation