Stochastic Generator of a New Family of Lifetime Distributions with Illustration

Accepted - March 2023

Abstract

In this article, a new family of lifetime distributions is introduced to help researchers model different types of data sets. Furthermore, the maximum likelihood method was used in estimating the model's parameters. Some structural properties of the distribution have been derived and studied. These are density function, distribution function, and reliability function, hazard rate function, moments, moment generating function, entropies, order statistics, Bonferroni and Lorenz curves. Simulation method was used to investigate the behaviors of the parameters of the proposed distribution; the results showed that the mean square error and standard error for the chosen parameter values decrease as the sample size increases. The proposed distribution was tested on real-life data, the results showed that the ET-exponential distribution performed better than other well-known distributions in modeling data. The results also showed that the distribution can be used as an alternative model in modeling lifetime processes.