الفهرس 
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Abstract
Although distributions have been developed, we are always looking for more flexible or appropriate distributions to keep pace with the modern era. This has been supported by researchers seeking to develop new, more flexible distributions. As a result, many new distributions have been developed and studied in previous years like bivariate discrete Weibull, bivariate discrete Rayleigh, bivariate discrete exponentiated, bivariate discrete inverse Weibull, bivariate geometric, inverse bivariate Poisson, and others. This thesis aims to introduce new, more flexible statistical distributions, which can be used in various fields such as sports competitions, engineering applications, etc.The thesis consists of three chapters:In chapter (1), we give a general introduction and historical background relevant to the literature survey. Also, we have provided some basic information about the probability distributions that have been used in this thesis. In addition, we discuss some different goodness of fit statistical tests such as the Akaike information criterion and Hannan-Quinn information criterion.In chapter (2), a new five-parameter bivariate discrete distribution called the bivariate discrete exponentiated Weibull distribution is introduced. Some statistical and reliability properties of the proposed discrete model have been derived. The maximum likelihood estimators of the parameters are deduced. Two real data sets have been analyzed using the new discrete distribution and compared with another famous distribution. It is clear from the comparison that the new distribution . It is the data sets better than some well-known distributions.The results of this chapter are contained in a paper with a title ” Bivariate Discrete Exponentiated Weibull Distribution: Statistical Properties, Estimation, Simulation and Applications ”. Accepted to publish in Springer journal editorial office in mathematical sciences.Finally, in chapter (3), we introduced a new three or more parameters bivariate discrete family distribution called the bivariate discrete generalized exponential-G family distribution. Some statistical and reliability properties of this family distribution have been derived. The maximum likelihood estimators of the parameters are deduced. real data sets are analyzed using the new family distribution compared with another well-known distribution. It is clear from the comparison that the new distribution is the best distribution for fitting the data sets from among all tested distributions.The results of this chapter are contained in a paper with a title ” Bivariate Discrete Odd Generalized Exponential Generator Of Distributions For Count Data: Copula Technique, Mathematical Theory, and Applications ”. Accepted to publish in axioms journal in mathematical sciences.