Bayesian probability

Physics

Exponential function

Mathematics

Principle of maximum entropy

Entropy (arrow of time)

Statistics

Mathematical optimization

Mean squared error

Mathematical analysis

Estimator

Computer science

Exponential distribution

Quantum mechanics

Bayes estimator

Applied mathematics

Entropy

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.

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