TY - JOUR
T1 - Probability and conditional moments of multivariate uniform random variables satisfying a linear inequality constraint
AU - Mignolet, Marc
AU - Lin, Chung Chih
N1 - Funding Information:
The partiat support of tl~ds work by a grant from t~e Allied-Signa! Aerospace Corporation ~s gratefafiy acknowledged. The authors also wish ~o tb._ank Dr E.C~ 1brig for a fruitful discussion of the problem and the reviewers for some constructive commen~s.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1992
Y1 - 1992
N2 - 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.
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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U2 - 10.1016/0266-8920(92)90010-F
DO - 10.1016/0266-8920(92)90010-F
M3 - Article
AN - SCOPUS:38249015549
VL - 7
SP - 65
EP - 74
JO - Probabilistic Engineering Mechanics
JF - Probabilistic Engineering Mechanics
SN - 0266-8920
IS - 2
ER -