Generalized exponential geometric extreme distribution

Abstract

ABSTRACTRecently, Louzada et al. proposed a new three-parameter distribution with decreasing, increasing, and unimodal hazard functions. They have provided several properties of the distribution, and discussed different inferential issues. In this article we discuss a generalized version of the model following the approach of Marshall and Olkin. The proposed model is more flexible than the Louzada–Marchi–Roman model, although they have the same number of parameters. The model has three unknown parameters, and the hazard function can take different shapes. We propose using the expectation–maximization (EM) algorithm to compute the maximum likelihood estimators of the unknown parameters. We further consider the bivariate generalization of the proposed model and discuss its different properties. The EM algorithm can be used to estimate the unknown parameters in case of the bivariate model also. One bivariate data set has been analyzed for illustrative purposes, and the performance is quite satisfactory.