الفهرس 
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Abstract
Recently, researchers have an increasing interest in generating new probability distributions to estimate the reliability function and survival function as a result of changing data patterns of studied phenomena and to obtain accuracy in studies and special research in the field of reliability.
Pappas et al. (2013) developed a new family to generate probability distributions called Alpha Algorithm Transformed Distribution.
In this Study, two new distributions were proposed: Alpha Algorithm Transformed Exponential Distribution and Alpha Algorithm Transformed Generalized Logistic Distribution whose equations, characteristics and methods of estimation were derived by the researchers, and with the help of maple and other high-level programming languages in performing operations Arithmetic, (arthmetic operations?)
Mahavi et al. (2017) and others introduced a new family to generate probability distributions called an Alpha Power Transformed distributions. Also, a number of researchers presented new distributions similar to Mahavi. For the current research, a new distribution was proposed along the lines of this family For him (of Mahava’s family?), namely, Alpha Power Transformed Kumaraswamy distribution, as well as derivations of its equations, characteristics and methods of estimation by the researcher and with the help of programming languages.
These new and previous distributions of these two families were applied to two sets of real data, the first group was lung cancer data that was obtained from Iraq - Baghdad, Al Amal Hospital for Cancer Diseases, and the second set of data was Wheaton data for the state of Canada, which is the Wheaton River data. Then, the researcher conducted a comparison between these distributions to find the best matching of data for the two groups. The results for the first group were that the best reconciliation of data is Alpha Algorithm Transformed Generalized Exponential Ponential distribution while for the second group was Alpha Algorithm Transformed Weibull distribution. The estimation methods for the new distributions were also compared and the results showed that the best estimation methods for both groups is maximum likelihood estimation method, depending on the comparison criteria mentioned in the first chapter.