Maxwell-Rayleigh Distribution and Its Applications

In this study, a new distribution was created, which is the Maxwell-Rayleigh distribution with two parameters (𝜃, 𝜆), using the (TX Family method), and some different characteristics of the Maxwell-Rayleigh distribution were studied, and the shape of the distribution was skewed towards the left, and its parameters were estimated using The weighted least squares method, and for the purpose of comparing the estimation methods for parameters, the Monte-Carlo simulation method was employed using the Wolfram Mathematica 12.2 program to conduct several experiments with different sample sizes (small "25,50", medium "100"). and large "150" and through the use of the statistical scale Mean Squares Error (MSE), and the results showed the preference of the weighted least squares method in estimating parameters, at medium and small sample sizes, and the preference of the method of greatest possibility at large sample sizes.