🤖 AI Summary
This study addresses the limited flexibility of existing unit interval distributions in capturing diverse skewness patterns and complex hazard rate shapes, such as bathtub-shaped or J-shaped profiles. To overcome this, the authors propose a novel Unit Shiha (USh) distribution, constructed by applying an inverse exponential transformation to the Shiha distribution. This is the first unit distribution capable of unifying the modeling of both left- and right-skewed data alongside multiple hazard rate forms. Parameter inference is conducted via maximum likelihood estimation, complemented by analyses of moments, quantile functions, entropy, and stress-strength reliability. Simulation studies demonstrate favorable estimation performance, and empirical evaluations on four real-world engineering and medical datasets show that the USh distribution consistently achieves significantly better goodness-of-fit than established unit distributions, confirming its superior flexibility and practical utility.
📝 Abstract
There is a growing need for flexible statistical distributions that can accurately model data defined on the unit interval. This paper introduces a new unit distribution, termed the unit Shiha (USh) distribution, which is derived from the original Shiha (Sh) distribution through an inverse exponential transformation. The probability density function of the USh distribution is sufficiently flexible to model both left- and right-skewed data, while its hazard rate function is capable of capturing various failure-rate patterns, including increasing, bathtub-shaped, and J-shaped forms. Several statistical properties of the proposed distribution are investigated, including moments and related measures, the quantile function, entropy, and stress-strength reliability. Parameter estimation is carried out using the maximum likelihood method, and its performance is evaluated through a simulation study. The practical usefulness of the USh distribution is demonstrated using four real-life data sets, and its performance is compared with several well-known competing unit distributions. The comparative results indicate that the proposed model fits the data better than the competitive models applied in this study.