An Extension of the UEHL Distribution Based on the DUS Transformation

Abstract

In this study, we propose a new distribution based on the Dinesh, Umesh, and Sanjay (DUS) transformation by using the Unit Exponentiated Half-Logistic (UEHL) distribution as the baseline distribution, a member of the family of proportional hazard rate models. Moreover, we study several properties, such as moments, skewness, kurtosis, stress-strength reliability, and likelihood ratio ordering. Further, we discuss the statistical inference on the parameters of the proposed distribution by the maximum likelihood estimation (MLE) method. Besides, we conduct a simulation based on the new distribution to investigate the behavior of the maximum likelihood estimates in various conditions. Furthermore, we present a numerical example to show the performance of the distribution on a real-life data set. Finally, we discuss the need for further research.

Üstellenmiş UEHL Dağılımı: Özellikler ve Uygulamalar

“…The data is called the reservoir data that is obtained from the monthly water capacity of the Shasta Reservoir in California (Nadar et al, 2013). We compare the performance of the EUEHL(𝜃𝜃, 𝜆𝜆, 𝛼𝛼) distribution with the Weibull, Beta, Kumaraswamy (Kumaraswamy, 1980), UEHL, and DUS-UEHL (Genç and Özbilen, 2023) distributions. The pdfs of the distributions that are used for comparison are given as follows:…”