Shiha Distribution: Statistical Properties and Applications to Reliability Engineering and Environmental Data

This paper introduces a new two-parameter distribution, referred to as the Shiha distribution, which provides a flexible model for skewed lifetime data with either heavy or light tails. The proposed distribution is applicable to various fields, including reliability engineering, environmental studies, and related areas. We derive its main statistical properties, including the moment generating function, moments, hazard rate function, quantile function, and entropy. The stress–strength reliability parameter is also derived in closed form. A simulation study is conducted to evaluate its performance. Applications to several real data sets demonstrate that the Shiha distribution consistently provides a superior fit compared with established competing models, confirming its practical effectiveness for lifetime data analysis.

💡 Research Summary

The paper introduces a new two‑parameter lifetime distribution, named the Shiha distribution, designed to model right‑skewed data with either heavy or light tails. The distribution is defined as a mixture of an exponential distribution with rate ω, an exponential distribution with rate 2ω, and a Gamma distribution with shape 2 and rate 2ω. The mixing weights are p₁ = ω/(ω + 3η), p₂ = η/(ω + 3η) and p₃ = 2η/(ω + 3η), where ω > 0 and η > 0. When η = 0 the model collapses to the simple exponential distribution Exp(ω).

Closed‑form expressions are derived for the probability density function, cumulative distribution function, survival function, and hazard rate. The hazard function is shown to be unimodal; its unique maximum occurs at y* = (1/ω)