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F. A. Shiha

Publications and source records attributed to F. A. Shiha.

8 recordsLinked to original sources
arXiv2026

Unit Shiha Distribution and its Applications to Engineering and Medical Data

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.

stat.ME↗
arXiv2026

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.

stat.ME↗
arXiv2023

Stirling numbers with higher level and records

In this present paper, we show that the Stirling numbers of the first kind with higher level connected with the probability distribution of the number of records and record times in the so-called F^α-scheme. In addition, we determine the location of the maximum of the Stirling numbers of the first kind with higher level.

math.PR↗
arXiv2019

The r-central factorial numbers with even indices

In this paper, we introduce the $r$-central factorial numbers with even indices of the first and second kind, as extended versions of the central factorial numbers with even indices of both kinds. We obtain several fundamental properties and identities related to these numbers. We show that the unsigned $r$-central factorial numbers with even indices of the first kind are strictly log-concave and Poisson-binomially distributed . Finally, we consider the $r$-central factorial matrices and the factorization of it.

math.CO↗
arXiv2017

A $q$-analogue of $\barα$-Whitney Numbers

We define the $(q,\bar{\boldsymbolα})$-Whitney numbers which are reduced to the $\bar{\boldsymbolα}$-Whitney numbers when $q\rightarrow1$. Moreover, we obtain several properties of these numbers such as explicit formulas, recurrence relations, generating functions, orthogonality and inverse relations. Finally, we define the $\bar{\boldsymbolα}$-Whitney-Lah numbers as a generalization of the $r$-Whitney-Lah numbers and we introduce their important basic properties.

math.CO↗
arXiv2016

The generalized r-Whitney numbers

In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of The relations between Whitney and Stirling numbers are given.

math.CO↗