A New Extension of Generalized Exponential Distribution with Application to Ozone Data

Abstract

In this article, a new distribution, called transformed Generalized Exponential Distribution () is proposed. The distribution has simple closed forms pdf and cdf. Several properties of the distribution are studied including unimodality, moments, conditional moments, stochastic ordering and Shannon entropy. The distribution is capable of monotonically increasing, decreasing, bathtub and upside down shaped hazard rates. Furthermore, we discussed several methods of estimation for estimating the parameters. In particular, we compare, through simulation study, the performance of the maximum likelihood estimation, maximum product spacing estimation, ordinary and weighted least-squares estimation methods. Also, the average interval lengths and coverage rates of 95% confidence intervals, including boot-p and boot-t confidence intervals for different parameter values are provided. A real data set is used to illustrate the applicability of the proposed distribution.