MAXIMUM LIKELIHOOD ESTIMATION OF THE KUMARASWAMY MARSHAL-OLKIN LINDELY -LOMAX DISTRIBUTION FROM TYPE II CENSORED SAMPLES | ||
| مجلة البØوث المالية والتجارية | ||
| Volume 26, Issue 4 - Serial Number 1, October 2025, Pages 338-375 PDF (894.25 K) | ||
| Document Type: المقالة الأصلية | ||
| DOI: 10.21608/jsst.2025.408110.2083 | ||
| Authors | ||
| Ø£Øمد أبو المعاطي* ; عبدالØميد عيسى* | ||
| قسم الإØصاء- كلية التجارة بنين -جامعة الأزهر | ||
| Abstract | ||
| Abstract This paper introduces and studies the Kumaraswamy Marshall–Olkin Lindley–Lomax (KMOLL) distribution, a new and flexible four-parameter lifetime model capable of capturing a variety of hazard rate shapes, including increasing, decreasing, bathtub, and unimodal forms. Several statistical properties of the KMOLL distribution are derived, including the probability density function (PDF), cumulative distribution function (CDF), survival and hazard functions, skewness, kurtosis, and moments. Estimation of the model parameters is explored through maximum likelihood estimation (MLE) under both complete and Type-II censored data. Additionally, alternative estimation techniques, such as Maximum Product of Spacings (MPS), Least Squares Estimation (LSE), Weighted Least Squares Estimation (WLSE), and Percentile Estimation (PE), are examined. A comprehensive simulation study is conducted to compare the performance of the estimators under various sample sizes and censoring levels. Finally, the applicability of the KMOLL model is illustrated using a real-life dataset, demonstrating its superior fitting capability compared to related models. Furthermore, the study highlights the model’s ability to accommodate data with diverse skewness and tail behavior, making it suitable for applications in fields such as reliability engineering, biomedical sciences, and actuarial analysis. The KMOLL distribution also demonstrates strong adaptability when handling censored data scenarios, enhancing its relevance in survival analysis contexts. The inclusion of the Marshall–Olkin and Lindley–Lomax mechanisms provides additional flexibility, enabling the model to capture complex real-world phenomena more accurately. Overall, the KMOLL model offers a robust and versatile statistical framework with significant potential for both theoretical development and practical implementation. | ||
| Keywords | ||
| Kumaraswamy distribution; Marshall–Olkin extension; Lindley distribution; Lomax distribution; Flexible lifetime models | ||
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