An extended life time distribution: theory, properties and applications

Abstract

This paper is an addition to the series of modification and improvement of the extant distributions which enable them to analyze the new emerging situations efficiently. We develop a new lifetime distribution by generalizing the Erlang truncated exponential distribution using the Topp Leone family of distributions. A comprehensive account of mathematical characteristics such as quantile function, moments, probability weighted moments, moment generating function, and probability generating function of the proposed distribution is presented. Some reliability measures such as hazard rate function, residual life function, and reversed residual life function are also provided. Several entropy measures including Reyni entropy, Tsallis entropy, cumulative Tsallis entropy, and dynamic cumulative Tsallis entropy are obtained. Besides, the extropy, residual extropy, and cumulative residual extropy are explored. The unknown parameters of the proposed distribution are estimated by using the maximum likelihood method. The stability of the model parameters is examined through the simulation study. The application of our proposed distribution is explained through three real-life examples and its performance is illustrated through its comparison with the competent existing distributions.