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.

翻译：对于能够准确建模定义在单位区间上的数据的灵活统计分布的需求日益增长。本文引入了一种新的单位分布，称为单位Shiha（USh）分布，该分布通过逆指数变换从原始的Shiha（Sh）分布推导而来。USh分布的概率密度函数具有足够的灵活性，能够对左偏和右偏数据进行建模，而其风险率函数则能够捕捉各种失效率模式，包括递增型、浴盆型和J型。本文研究了所提出分布的若干统计性质，包括矩及相关度量、分位数函数、熵以及应力-强度可靠性。参数估计采用最大似然法进行，并通过模拟研究评估其性能。利用四个真实数据集证明了USh分布的实际有效性，并将其性能与几种著名的竞争性单位分布进行了比较。对比结果表明，所提出的模型比本研究中应用的竞争模型能更好地拟合数据。