الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The aim of this thesis is to propose a new class of distribution which is consider an extension of the inverse Weibull distribution which offers a more flexible distribution for modeling lifetime data. We extend the inverse Weibull distribution by Marshall-Olkin method (MOEIW). Some statistical properties of the MOEIW are explored, such as reliability, quantiles, moments, order statistics and Lorenz curves. Moreover, the estimation of the MOEIW parameters is discussed by using Maximum Likelihood Estimation method. In addition, the estimation of the stress-strength parameters is discussed. The proposed extended model is applied on real data and the results are given which illustrate the superior performance of the MOEIW distribution compared to other related models. The proposed distribution generalizes many distributions that are commonly used in life testing and in the analysis of lifetime data. Some of these distributions that can be derived from the proposed MOEIW distribution include: inverse Weibull (IW), Frechet (F), inverse Rayleigh (IR) and inverse exponential (IE) distributions. Other aim of this thesis is to specify the suitable methods for estimating the parameters of MOEIW distribution. So, the performance of different estimation methods called non-Bayesian estimation (maximum likelihood, Percentiles, least squares, weighted least-squares, Cramer-van Mises and Anderson-Darling) and Bayesian estimation (square error and LINEX), is compared in terms of the bias and mean squared error through numerical simulations and real data. Moreover, we introduces two popular parameters estimation methods, namely E-Bayesian estimation and hierarchical Bayesian estimation to estimate parameter and reliability of the inverse Weibull (IW) distribution. The formulas of E-Bayesian and hierarchical Bayesian estimations of the parameter and reliability are obtained in closed forms. To illustrate the applicability of the obtained results, simulated and real data are used which illustrate that the E-Bayesian estimate is better than the hierarchical Bayesian for the estimate of the parameter and reliability of the IW distribution.