Constructing a New Weighted Maxwell Probability Distribution with Comparing ofits two Parameters

Abstract This paper discuss the Maxwell distribution with scale parameter (θ), and how to expand this family to find weighted Maxwell p.d.f which is necessary for sampling from population of different sizes, so we apply some transformation on [f_T (t;θ)] to obtain [g_w (t)], then its C.D.F obtained. Also the formula for r^th moments about origin also derived to help in finding moment estimators of (β). Keywords: Rayleigh distribution, Weighted Maxwell, Gamma Function, Cumulative distribution function, length biased moments, L – Moment, MLE