Power unit exponential probability distribution: Statistical inference and applications

We introduce a generalized version of a unit distribution called power unit exponential probability distribution (PUEPrD) using the power transformation of the unit exponential probability distribution. Some statistical properties of the proposed distribution are derived. For some selected parameter cases, we have demonstrated that the hazard function of the proposed distribution can be shaped by increasing and bathtub curves. Twelve estimation methods such as maximum likelihood, Anderson-Darling, Cramer-von-Mises, maximum product spacings, least squares, weighted least squares, right tail Anderson Darling, left-tail Anderson Darling, minimum spacing absolute distance, minimum spacing absolute-log distance, Anderson Darling left-tail second order, Kolmogorov are used to estimate the parameters of the suggested distribution. A numerical simulation study is conducted to check the efficiency of the parameter estimates of the proposed model. With the help of some real-life data sets, the flexibility and usefulness of the PUEPrD are illustrated. As a result of two real data analyses, we observe that the fit of the proposed distribution to the data is superior to its competitors according to the examined criteria.