The Unit Arcsine–Exponential Distribution and Its Statistical Properties with Inference and Application to Reliability Data

This paper presents a new continuous data model, the Unit Arcsine–Exponential distribution (UASED), a flexible data model on the unit interval. It is built up by an exponential-based arcsine-type transformation to allow it to represent a very wide range of shapes that can be used to model proportions and rates. A number of basic properties are obtained, such as closed-form formulas of the quantile function, moments, and entropy measures. Maximum likelihood and maximum product of spacings methods are developed to estimate parameters, and their performance is determined by Monte Carlo simulation, which shows that these methods can reasonably estimate the parameters and be stable over a variety of different parameter settings. To demonstrate that a model is practically useful, an application to real-world data on the reliability of devices in terms of failure time is discussed. The findings indicate that the UASED is a good fit to the data, in the sense that it is effective in terms of skewness and tail behavior and compares well or competes favorably with current unit distributions. All in all, the suggested model is a sparse alternative to model bounded data with sound inferential characteristics and high practical utility.