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Abstract
            The Weibull distribution has been used over the past decades for modeling data in many fields so finding generalization of the Weibull distribution becomes very useful to fit more cases or get better fits than before. In this paper, the Kumaraswamy Kumaraswamy Weibull (Kw Kw W) distribution is presented for the first time and we show that it is generalizes many important distribution. The probability density function (pdf), the cumulative distribution function (cdf), moments, quantiles, the median, the mode, the mean deviation, the entropy, order statistics, L-moments, extreme value and parameters estimation based on maximum likelihood are obtained for the Kumaraswamy Kumaraswamy Weibull distribution. A simulation study and a real data set is used to illustrate the potentiality and application of the new Kumaraswamy Kumaraswamy Weibull distribution.
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