### 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 |

### Fingerprint

### 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.

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 -