PDF Method Deriving Distribution for Transformation

Method

• Assume $Y=h(X)$ for Continuous Injective function $h$
• Assume PDF $f_X(x)$ is known, but there is no closed-form CDF
• PDF of $Y$ given by: $f_Y(y)=\frac{f_X(h^{-1}(y))}{|h^{\prime }(h^{-1}(y))|}$