Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

Finding the best fitted distribution for data set becomes practically an important problem in world of data sets so that it is useful to use new families of distributions to fit more cases or get better fits than before. In this thesis, a new generating family of generalized distributions so called the Kumaraswamy - Kumaraswamy (Kw Kw) family is presented. Four important common families of distributions are illustrated as special cases from the Kw Kw family. Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics are obtained. Parameters estimation and variance covariance matrix are obtained using maximum likelihood method. The Kumaraswamy - Kumaraswamy Weibull (Kw Kw Wi) distribution is derived, as a special case from the Kw Kw familly, and we show that it generalizes many important distribution. The pdf, the cdf, moments, quantile, the median, the mode, the mean deviation, the entropy, order statistics, L-moments, extreme value and unknown parameters estimation based on maximum likelihood are obtained for the Kw Kw Wi distribution. A simulation study and a real data set are used to illustrate the potentiality and applications of the new Kw Kw Wi distribution

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