Using the Transformation Method to Evaluate The Probability Density Function of z = xα yβ

In this research, our objective is to evaluate the probability density function of z = xαyβ, where, x and y are two independent random variables, by using the probabilistic transformation method. The Probabilistic Transformation Methods (PTM) evaluate the Probability Density Function (PDF) of a function by multiplying the input pdf by the Jacobian of the inverse function. A new theorem for two input and one output has been developed. The result of our method is verified by the Monte Carlo simulation.