Transmuted Erlang-Truncated Exponential Distribution

Abstract

Abstract This article introduces a new lifetime distribution called the transmuted Erlang-truncated exponential (TETE) distribution. This new distribution generalizes the two parameter Erlang-truncated exponential (ETE) distribution. Closed form expressions for some of its distributional and reliability properties are provided. The method of maximum likelihood estimation was proposed for estimating the parameters of the TETE distribution. The hazard rate function of the TETE distribution can be constant, increasing or decreasing depending on the value of the transmutation parameter Φ ⁢ [ - 1 , 1 ] ${\Phi[-1,1]}$ ; this property makes it more reasonable for modelling complex lifetime data sets than the ETE distribution that exhibits only a constant hazard rate function. The goodness of fit of the TETE distribution in analyzing real life time data was investigated by comparing its fit with that provided by the ETE distribution and the results show that the TETE distribution is a better candidate for the data. The stability of the TETE distribution parameters was established through a simulation study.