Probability and conditional moments of multivariate uniform random variables satisfying a linear inequality constraint

Marc Mignolet; Chung Chih Lin

doi:10.1016/0266-8920(92)90010-F

Probability and conditional moments of multivariate uniform random variables satisfying a linear inequality constraint

Marc Mignolet, Chung Chih Lin

IAFSE-SEMTE: Mechanical and Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A computational technique is presented to evaluate a class of probabilities and expectations of multivariate uniform random variables encountered in the analysis of certain random mechanical systems. First, a finite series representation is derived for the probability that a linear combination of n independent random variables uniformly distributed in the interval [0, 1] does not exceed a given threshold. This exact representation is then used to obtain closed from expressions for various moments, means in particular, of uniform random variables conditional on a linear inequality constraint. Finally, various practical implementation aspects of these computations are discussed and a comparison with the Monte Carlo simulation method is conducted that validates the use of the proposed technique.

Original language	English (US)
Pages (from-to)	65-74
Number of pages	10
Journal	Probabilistic Engineering Mechanics
Volume	7
Issue number	2
DOIs	https://doi.org/10.1016/0266-8920(92)90010-F
State	Published - 1992

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Civil and Structural Engineering
Nuclear Energy and Engineering
Condensed Matter Physics
Aerospace Engineering
Ocean Engineering
Mechanical Engineering

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AB - A computational technique is presented to evaluate a class of probabilities and expectations of multivariate uniform random variables encountered in the analysis of certain random mechanical systems. First, a finite series representation is derived for the probability that a linear combination of n independent random variables uniformly distributed in the interval [0, 1] does not exceed a given threshold. This exact representation is then used to obtain closed from expressions for various moments, means in particular, of uniform random variables conditional on a linear inequality constraint. Finally, various practical implementation aspects of these computations are discussed and a comparison with the Monte Carlo simulation method is conducted that validates the use of the proposed technique.

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