الفهرس 
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Abstract
ABSTRACT : In the literature of distribution theory, a vast proportion is acquired by modifying continuous distributions and their applications in real-world phenomena. However, in a rapidly changing technological era, the data generated is becoming increasingly complex day by day, making it difficult for us to capture various aspects of this real data through existing continuous models. In view of this, we propose new flexible distributions ”univariate and bivariate” with their applications in different fields. After introducing the modified models, some of their statistical and reliability properties have been discussed in detail, especially, the hazard rate function. The general content of the thesis is presented in four chapters that are devoted to present, definitions and basic concepts, exponentiated generalized inverse flexible Weibull distribution, an extended to Gompertz distribution, and bivariate exponentiated inverse flexible Weibull extension distribution, respectively. The first chapter : includes some definitions and basic concepts in statistics. The objective of chapter two: is to propose a new 4-parameter exponentiated generalized inverse flexible Weibull distribution. Some of its statistical properties are studied. The model parameters are estimated via several approaches, namely, maximum likelihood, maximum product spacing and Bayesian. According to Bayesian approach, several techniques are used to get the Bayesian estimators, namely, Linex loss function and entropy loss function. The estimation herein is based on complete and censored samples. Markov Chain Monte Carlo simulation is used to discuss the behavior of the estimators for each approach. Finally, two real data sets are analyzed to obtain the flexibility of the proposed model. The results in this chapter are contained in a paper with a title ” Exponentiated Generalized Inverse Flexible Weibull Distribution: Bayesian and Non-Bayesian Estimation under Complete and Type II Censored Samples with Applications ”. Accepted to publish in Communications in Mathematics and Statistics ”ISI: Q1”. Https://doi.org/10.1007/s40304-020-00225-4.Our aim in the third chapter: is to propose a new three-parameter alternative to exponential and Gompertz distributions. The new model can be applied in modeling survival data, reliability systems and fatigue life studies. We derive explicit expressions for some of its statistical properties including quantities, hazard rate function, moments, moment of residual and reversed residual life. The parameters are estimated using the maximum likelihood method based on complete and type II right censored samples. We assess the performance of estimators in terms of bias and mean square error using simulation study. Finally, three real data sets are analyzed to illustrate the flexibility of the proposed model. The results in this chapter are contained in a paper with a title ”An extension to Gompertz model with its applications” Journal of Statistics Applications and Probability. To appear. Finally, in chapter four: a new bivariate exponentiated inverse flexible Weibull extension distribution is introduced. This model is of Marshall-Olkin type. The marginals of the new bivariate distribution have the exponentiated modified Weibull extension distribution which proposed by Sarhan et al. (2013). 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 effectively in fitting and analyzing real lifetime data than other well-known models. The results in this chapter are contained in a paper with a title ”Bivariate exponentiated inverse flexible Weibull extension distribution”. Journal of applied probability and statistics. To appear.