Power-Modified Kies-Exponential Distribution: Properties, Classical and Bayesian Inference with an Application to Engineering Data

We introduce here a new distribution called the power-modified Kies-exponential (PMKE) distribution and derive some of its mathematical properties. Its hazard function can be bathtub-shaped, increasing, or decreasing. Its parameters are estimated by seven classical methods. Further, Bayesian estimation, under square error, general entropy, and Linex loss functions are adopted to estimate the parameters. Simulation results are provided to investigate the behavior of these estimators. The estimation methods are sorted, based on partial and overall ranks, to determine the best estimation approach for the model parameters. The proposed distribution can be used to model a real-life turbocharger dataset, as compared with 24 extensions of the exponential distribution.

Automated summary

This paper introduces a new distribution called the power-modified Kies-exponential (PMKE) distribution and investigates its mathematical properties. The parameters of this distribution are estimated using seven classical methods and Bayesian estimation methods. Simulation results are provided to examine the performance of these estimators and the best estimation approach is determined based on ranking. The proposed distribution can be used to model a real-life turbocharger dataset and is compared with 24 extensions of the exponential distribution.