# Estimating and Validating the Cumulative Distribution of a Function of Random Variables: Toward the Development of Distribution Arithmetic

Estimating and Validating the Cumulative Distribution of a Function of Random Variables: Toward... A method for estimating and validating the cumulative distribution of a function of random variables (independent or dependent) is presented and examined. The method creates a sequence of bounds that will converge to the distribution function in the limit for functions of independent random variables or of random variables of known dependencies. Moreover, an approximation is constructed from and contained in these bounds. Preliminary numerical experiments indicate that this approximation is close to the actual distribution after a few iterations. Several examples are given to illustrate the method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Estimating and Validating the Cumulative Distribution of a Function of Random Variables: Toward the Development of Distribution Arithmetic

, Volume 9 (2) – Oct 17, 2004
15 pages

/lp/springer_journal/estimating-and-validating-the-cumulative-distribution-of-a-function-of-C0QqGFycHX
Publisher
Springer Journals
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1023090317875
Publisher site
See Article on Publisher Site

### Abstract

A method for estimating and validating the cumulative distribution of a function of random variables (independent or dependent) is presented and examined. The method creates a sequence of bounds that will converge to the distribution function in the limit for functions of independent random variables or of random variables of known dependencies. Moreover, an approximation is constructed from and contained in these bounds. Preliminary numerical experiments indicate that this approximation is close to the actual distribution after a few iterations. Several examples are given to illustrate the method.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 17, 2004

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