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 | |
| State | Published - 1992 |
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ASJC Scopus subject areas
- Mechanical Engineering
- Safety, Risk, Reliability and Quality
Cite this
Probability and conditional moments of multivariate uniform random variables satisfying a linear inequality constraint. / Mignolet, Marc; Lin, Chung Chih.
In: Probabilistic Engineering Mechanics, Vol. 7, No. 2, 1992, p. 65-74.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Probability and conditional moments of multivariate uniform random variables satisfying a linear inequality constraint
AU - Mignolet, Marc
AU - Lin, Chung Chih
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.
UR - http://www.scopus.com/inward/record.url?scp=38249015549&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38249015549&partnerID=8YFLogxK
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 -