الفهرس 
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Abstract
Statistical distributions are very useful in describing and predicting real world phenomena. Although many distributions have been developed, there is always room for developing distributions which are either more flexible or for fitting specific real world scenarios. This has motivated researchers seeking and developing new and more flexible distributions. As a result, many new distributions have been developed and studied in the previous years. The aim of this thesis is to introduce a new family of statistical distributions, which can been used to describe the lifetime of a physical systems, engineering applications and many different fields.The thesis consists of five chapters: In Chapter 1, we give a general introduction and historical background relevant to literature survey. In addition, we have provided some basic information about the probability distributions that have been used in this thesis. In addition, we discusses some different goodness of fit statistical tests such as Kolmogorov-Smirnov test, Akaike information criterion, Correct Akaike information criterion and the Bayesian information criterion.In Chapter 2, a new three-parameter model is introduced. We called it the exponentiated flexible Weibull extension (EFW) distribution. Several properties of this distribution have been discussed. We applied the maximum likelihood method to estimate the parameters. In addition, asymptotic confidence bounds of the parameters are discussed. Two real data sets are analyzed using the new model, which show that the new model fits the data better than some other very well known-models.In Chapter 3, a new two parameter model is introduced, which is the distribution of the reciprocal of a random variable that has the flexible Weibull extension distribution as was done for the inverse Weibull distribution. We called it the inverse .exible Weibull extension (IFW) distribution. Several properties of this distribution have been discussed. The maximum likelihood estimators of the parameters are derived. Two real data sets are analyzed using the new model, which show that the new model .ts the data better than some other very well-known models.In Chapter 4, we propose a new three-parameter model by exponentiating the inverse flexibleWeibull extension distribution given in chapter (3). We called it the Exponentiated inverse flexible Weibull extension (EIFW) distribution. Several properties of this distribution have been discussed such as the probability density function, quantiles, median, modes, moments, moment generating function, survival function, failure rate function, reversed hazard rate function, mean time to failure, mean time to repair and mean time between failures. The maximum likelihood estimators of the parameters are derived. Two real data sets are analyzed using the new model, which show that the new model fits the data better than some other very well-known models.Chapter 5, a new bivariate model is introduced. We called it the bivariate exponentiated modi.ed Weibull extension () distribution. This model is of Marshall-Olkin type. The marginals of the new bivariate distribution have exponentiated modi.ed Weibull extension distribution that was proposed by Sarhan et al. The joint probability density function and the joint cumulative distribution function are given in closed forms. Several properties of this distribution have been discussed. The maximum likelihood estimators of the parameters are derived. One real data set is analyzed using the new bivariate distribution, which shows that the new model can be used quite e¤ectively in .tting and analyzing real lifetime data better than the bivariate generalized Gompertz distribution.