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Statistics is one of the important sciences in our life today, it enters in all disciplines. In this book we take one of the important distributions (GED) with one and double weighted functions as: Deriving pdf and cdf and all properties for the new distribution we obtained (WGED) and (DWGED). Deriving the moments and moment generating function, then estimate the scale parameter for(DWGED)in two methods [ MOM, MLE ], and compared between these two estimates to know which one is the best by simulation, with minimum MSE.