In this paper, the probability d istribution (Generalized Ray leigh) with t wo parameters (θ, σ 2), in case of outlier, is developed, where the probability density function (. .) is defined, and its mo ment generating function is derived, to help us in finding the moments, also its cumulative distribution function is found to be used, in obtaining the least squares estimator of the parameters σ 2 and θ. The parameters are estimated also by method of mo ments and method of least square, and also mixture of the estimators are derived, and explained, the estimators of maximu m likelihood for θ, σ 2 are also obtained.