A new truncated (0, b)-F family of lifetime distributions with an extensive study to a submodel and reliability data

In this paper, a new truncated (0, b )-F family of lifetime distributions is introduced. Its main interest is to provide simple and flexible probability density functions with a bounded support without introducing non-explicit normalization constants, unlike the family based on the classical truncation technique. A detailed examination of a subdistribution known as the (0, b )-exponential distribution is carried out. Among its features, this distribution has unimodal, left-skewed, and decreasing shapes for the probability density function, while it has increasing and convex shapes for the corresponding hazard rate function. The distribution’s properties are studied in depth, including moments, quantiles, and first-order stochastic dominance. Maximum likelihood estimates of the distribution parameters are obtained. Furthermore, a simulation study is conducted to gain some information on the performance of these estimates. Fitting two reliability data sets demonstrates the model’s utility among alternative models via some measures of goodness-of-fit.