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In this paper, a new method is proposed for adding two parameters to a continuous distribution that extends the methods of [5] and [14] for adding a parameter to a family of distributions. Using the added parameters, the skewness and kurtosis of the resulting family can be fully controlled. Also simple sufficient conditions for the shape of the density and hazard rate functions of the new family are provided. Finally, the new method is applied in particular, to the one parameter Burr XII distribution to yield a three parameter extended Burr XII distribution which may serve as a competitor to such commonly used three parameters families of distributions such as generalized gamma and inverse Gaussian distributions.

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