### Journals Information

**
Mathematics and Statistics Vol. 11(6), pp. 936 - 942 DOI: 10.13189/ms.2023.110608 Reprint (PDF) (804Kb) **

## Generalized Half-Logistic Distribution Using Linear Regression Model

**Ahmed Al-Adilee ^{1}, Wasan Al-Shemmari ^{2}^{,*}**

^{1}Department of Mathematics, Faculty of Education, University of Kufa, Iraq

^{2}Department of Mathematics, Faculty of Education for Girls, University of Kufa, Iraq

**ABSTRACT**

In this study, the generalized half-logistic distribution (GHLD) was expanded by replacing the shape parameter with a linear model, denoted by the notation . This model involves a vector of explanatory variables denoted by , where with a vector of coefficients of each one of those explanatory variables, denoted by . The linear model represents several explanatory variables with their coefficients that represent effects on some items. Briefly, the proposed distribution is denoted by, LM-GHLD. Afterward, by finding the pdf, and cdf of LM-GHLD, many mathematical and statistical characteristics were investigated, such as the survival function, the hazard function, the moments, the moment generating function, quantiles, the Rényi entropy, and the order statistic function. The unknown parameters of the modern distribution were estimated with the non-Bayesian method, which is known as the Maximum Likelihood Estimate (MLE). An important part of such a study is related to the simulation, which is shown within a generation of different sample sizes. A goodness-of-fit measure has been implemented on real data sets to compare the classical distribution (GHLD) and the proposed distribution (LM-GHLD) enabling us to determine which distribution is better. Eventually, we provide some conclusions and summarize our findings.

**KEYWORDS**

Continues Distributions, Generalized Half-Logistic Distribution, Linear Regression Model, Moments, Non-Bayesian Methods

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Ahmed Al-Adilee , Wasan Al-Shemmari , "Generalized Half-Logistic Distribution Using Linear Regression Model," Mathematics and Statistics, Vol. 11, No. 6, pp. 936 - 942, 2023. DOI: 10.13189/ms.2023.110608.

(b). APA Format:

Ahmed Al-Adilee , Wasan Al-Shemmari (2023). Generalized Half-Logistic Distribution Using Linear Regression Model. Mathematics and Statistics, 11(6), 936 - 942. DOI: 10.13189/ms.2023.110608.