Maximum Likelihood Estimation Of The kumaraswamy Marshal–Olkin Flexible Weibull Extension Distribution under Type-II Censored Samples

Metawally, Nader; Abou Almaaty, Ahmed; Eisa, Abd El-Hamid

doi:10.21608/skjaz.2023.455911

Maximum Likelihood Estimation Of The kumaraswamy Marshal–Olkin Flexible Weibull Extension Distribution under Type-II Censored Samples

نوع المستند : أبحاث علمية

المؤلفون

¹ Department of Statistics, Faculty of Commerce, Al-Azhar University, Cairo, Egypt; mu.nader.sh2010@gmail.com

² Department of Statistics, Faculty of Commerce, Al-Azhar University,Cairo, Egypt;Ahmedabouelmaaty.22@azhar.edu.eg

³ Department of Statistics, Faculty of Commerce, Al-Azhar University, Cairo, Egypt;abdo.easa2012@gmail.com

10.21608/skjaz.2023.455911

المستخلص

Abstract:
This study presents the Kumaraswamy Marshal–Olkin Flexible Weibull Extension (KMO-FWE) distribution, a newly developed probability model designed to extend existing lifetime distributions. This extension enhances the ability to model various hazard rate patterns with greater flexibility. The study explores the fundamental properties of this distribution, including the cumulative distribution function (CDF), probability density function (PDF), survival function, hazard function, moments, moment generating function, quantile function, and order statistics. To estimate the distribution’s parameters, several statistical methods are assessed, with a primary focus on Maximum Likelihood Estimation (MLE). Additionally, alternative estimation techniques such as Maximum Product Spacing (MPS), Least Squares (LS), Weighted Least Squares (WLS), and Percentile Estimation (PE) are considered. A Monte Carlo simulation study is conducted to evaluate the accuracy and efficiency of these estimation approaches under both complete data and Type-II censoring conditions. The results indicate that MLE is highly effective for large sample sizes but may introduce bias in smaller samples. In contrast, MPS provides stable parameter estimates under more complex conditions. While LS and WLS are computationally straightforward, their performance diminishes in the presence of censoring. Meanwhile, PE proves beneficial in reliability analysis based on percentile estimation. Overall, the findings highlight the KMO-FWE distribution as a versatile and reliable model, suitable for applications in reliability engineering, survival analysis, and biomedical research.

الكلمات الرئيسية