SACM - Egypt
Permanent URI for this collectionhttps://drepo.sdl.edu.sa/handle/20.500.14154/9653
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Item Restricted Lomax Distribution: Properties, Inference, and Applications(Saudi Digital Library, 2026) AlMutairi, Nadiyah Munahi Ghazai; Abu Sabh Aly, Amany ElAzazy; Abdelaziz Ali, Mohammed YusufThis thesis investigates the statistical properties, inference methods, and practical applications of the Lomax distribution under progressive Type-II censoring schemes. The study focuses on estimating the distribution parameters, the reliability function, and the reversed hazard rate function using both Bayesian and classical inference approaches. Maximum Likelihood Estimation (MLE) is employed as the non-Bayesian method, while Bayesian estimation is developed under informative and non-informative prior distributions. Several loss functions are considered, including the Squared Error Loss Function (SELF), Linear Exponential Loss Function (LINEX), and General Entropy Loss Function (GELF), to evaluate the efficiency and flexibility of Bayesian estimators. Since analytical solutions are often difficult to obtain, Lindley’s approximation and Markov Chain Monte Carlo (MCMC) techniques are utilized to approximate posterior distributions and Bayes estimates. In addition, Monte Carlo simulation studies are conducted to assess the performance of the proposed estimators under different sample sizes and censoring schemes. The results demonstrate that Bayesian estimators generally outperform maximum likelihood estimators in terms of Mean Squared Error, especially when informative prior information is incorporated. The study also highlights the suitability of the Lomax distribution for modeling reliability data, heavy-tailed phenomena, and lifetime observations encountered in engineering, medical, actuarial, and risk analysis applications.7 0