Implicit function density computation

TL;DR

This paper discusses a method for computing the distribution of a variable X from another variable A when they are related by a strictly monotone differentiable function, simplifying the process of density computation.

Contribution

It introduces a technique to derive the density of X directly from the density of A using the inverse of the monotone function f.

Findings

Density of X can be obtained from the density of A using the inverse function of f.

The method simplifies density computation for functionally related variables.

Applicable to any strictly monotone differentiable functions.

Abstract

If two random variables X and A are functionally related via f(X)=A for some strictly monotone continuously differentiable function f:R->R, the distribution of X may easily be computed from the distribution of A.