Modification of two Parameters Rayleigh into three Parameters one Through Exponentiated

Abstract

The continuous probability Rayleigh distribution is one of the important Is an important distribution  that can be used To analyze signal data and statistical error data as well as time to failure, so we work on modifying two parameters Rayleigh ( ) into three parameters one’s ( ) through exponentiated, the new  obtained, also the formula for r^th moments about origin is derived, to be used in estimating of parameters and also of reliability function. All derivation required were explained and the estimators by maximum likelihood and moments were obtained using different sets of initial values and the replicate of each experiment is ( ), the results are compared by using mean squared error (MSE).