Cumulative Distribution Functions and UPM/LPM Analysis

46 Pages Posted: 19 Sep 2012 Last revised: 16 Mar 2018

See all articles by Fred Viole

Fred Viole

OVVO Financial Systems; Fordham University

David N. Nawrocki

Villanova University - Department of Finance

Date Written: September 18, 2012

Abstract

We show that the Cumulative Distribution Function (CDF) is represented by the ratio of the lower partial moment (LPM) ratio to the distribution for the interval in question. The addition of the upper partial moment (UPM) ratio enables us to create probability density functions (PDF) for any function without prior knowledge of its characteristics. We are able to replicate discrete distribution CDFs and PDFs for normal, uniform, poisson, and chi-square distributions, as well as true continuous distributions. This framework provides a new formulation for UPM/LPM portfolio analysis using co-partial moment matrices which are positive symmetrical semi-definite, aggregated to yield a positive symmetrical definite matrix.

Keywords: Partial moments, CDF, PDF, Normal Distribution, Continuous Variable Estimates

JEL Classification: C13, C14

Suggested Citation

Viole, Fred and Nawrocki, David N., Cumulative Distribution Functions and UPM/LPM Analysis (September 18, 2012). Available at SSRN: https://ssrn.com/abstract=2148482 or http://dx.doi.org/10.2139/ssrn.2148482

Fred Viole (Contact Author)

OVVO Financial Systems ( email )

NJ
United States

Fordham University ( email )

113 West 60th Street
New York, NY 10023
United States

David N. Nawrocki

Villanova University - Department of Finance ( email )

800 Lancaster Avenue
Villanova, PA 19085-1678
United States
610-519-4323 (Phone)
610-519-6881 (Fax)

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