Maximum Likelihood Estimation Of The kumaraswamy Marshal–Olkin Flexible Weibull Extension Distribution under Type-II Censored Samples
Metawally, N., Abou Almaaty, A., Eisa, A. (2023). Maximum Likelihood Estimation Of The kumaraswamy Marshal–Olkin Flexible Weibull Extension Distribution under Type-II Censored Samples. EKB Journal Management System, 71(71), 33-66. doi: 10.21608/skjaz.2023.455911
Nader Metawally; Ahmed Abou Almaaty; Abd El-Hamid Eisa. "Maximum Likelihood Estimation Of The kumaraswamy Marshal–Olkin Flexible Weibull Extension Distribution under Type-II Censored Samples". EKB Journal Management System, 71, 71, 2023, 33-66. doi: 10.21608/skjaz.2023.455911
Metawally, N., Abou Almaaty, A., Eisa, A. (2023). 'Maximum Likelihood Estimation Of The kumaraswamy Marshal–Olkin Flexible Weibull Extension Distribution under Type-II Censored Samples', EKB Journal Management System, 71(71), pp. 33-66. doi: 10.21608/skjaz.2023.455911
Metawally, N., Abou Almaaty, A., Eisa, A. Maximum Likelihood Estimation Of The kumaraswamy Marshal–Olkin Flexible Weibull Extension Distribution under Type-II Censored Samples. EKB Journal Management System, 2023; 71(71): 33-66. doi: 10.21608/skjaz.2023.455911

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

مجلة مركز صالح كامل للإقتصاد الإسلامى بجامعة الأزهر
Volume 71, Issue 71, January 2023, Pages 33-66    PDF (1.02 M)
Document Type: أبحاث علمية
DOI: 10.21608/skjaz.2023.455911
Authors
Nader Metawally1; Ahmed Abou Almaaty2; Abd El-Hamid Eisa3
1Department of Statistics, Faculty of Commerce, Al-Azhar University, Cairo, Egypt; mu.nader.sh2010@gmail.com
2Department of Statistics, Faculty of Commerce, Al-Azhar University,Cairo, Egypt;Ahmedabouelmaaty.22@azhar.edu.eg
3Department of Statistics, Faculty of Commerce, Al-Azhar University, Cairo, Egypt;abdo.easa2012@gmail.com
Abstract
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.
Keywords
Key wards: Kumaraswamy Marshal–Olkin Flexible Weibull Extension; Maximum Likelihood Estimation; Monte Carlo Simulation; Reliability Analysis; Type-II Censoring
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