الفهرس | Only 14 pages are availabe for public view |
Abstract In this thesis, the problems of estimating the unknown parameters and prediction of future observations are considered when the lifetime units follow an extended Weibul (EW) distribution under ramp stress accelerated life testing (RS-ALT) in the presence of adaptive type-II progressive censoring (A-II-PC) samples. Thus, this thesis is divided into two main parts. In part one, both classical and Bayesian approaches are adopted to obtain point and interval estimators for the parameters and the acceleration factors. Under classical approach, three algorithms called scoring, expectation-maximization (EM), and stochastic expectation-maximization (SEM) algorithms are applied and the associated asymptotic and bootstrap condence intervals (CIs) are derived. While an extension of Hamiltonian Monte Carlo (HMC) method, called No-U-Turn Sampler (NUTS) is implemented through Stan software to obtain Bayesian point and interval estimates. In part two, one-sample and two-sample prediction problems are discussed from Bayesian and classical viewpoints. Under the latter, point prediction estimators are obtained using the best unbiased predictor (BUP) and conditional median predictor (CMP) while interval prediction estimators are constructed using a pivotal quantity. Concerning Bayesian method, two dierent methods based on NUTS applied by Stan are used to compute point and interval prediction estimates. To assess the performance of the suggested methods in this thesis, a Monte Carlo simulation study is conducted and revealed that all the proposed methods display good and close performance either under point or interval estimation and prediction. However, Bayesian approach shows superiority over classical approach under parameter estimation. While, the latter slightly outperforms the former in case of predicting the future observations under one-sample and two-sample problems. To illustrate the applicability of the methods provided in this thesis in reality, a real data example is presented and discussed. In this example, a new goodness of t test proposed by Gaigall (2019) in case of multi-samples is applied and proved a good t for the EW distribution in representing RS-ALT data. |