12 Pages Posted: 8 Dec 2012 Last revised: 16 Jul 2017
Date Written: December 7, 2012
We define the relationship between integration and partial moments through the integral mean value theorem. The area of the function derived through both methods share an asymptote, allowing for an empirical definition of the area. This is important in that we are no longer limited to known functions and do not have to resign ourselves to goodness of fit tests to define f(x). Our empirical method avoids the pitfalls associated with a truly heterogeneous population such as nonstationarity and estimation error of the parameters. Our ensuing definition of the asymptotic properties of partial moments to the area of a given function enables a wide array of equivalent comparative analysis to linear and nonlinear correlation analysis and calculating cumulative distribution functions for both discrete and continuous variables.
Keywords: Lebesgue, partial moments, continuous distribution,asymptotic
JEL Classification: C14, C60
Suggested Citation: Suggested Citation