### Abstract

In general , the exact probability distribution of a definite
non-Gaussian random field is not known. Some information about
this unknown distribution can be obtained from the 3rd and 4th
moment of the integral. Approximations to these moments are
calculated by a numerical technique based on recursive application
of Winterstein approximations) moment fitted linear combinations
of Hermite Polynomials of standard Gaussian variables). By use of
computerized symbol manipulations it is practicable to obtain
exact moments (up to order 4) of partial weighted sums of mutually
dependent variables with known moments (including mixed moments)
as fx log-normal variables or polynomials of standard Gaussian
variables. This sceme is used when calculating the moments of the
integral (and eventually approximating the integral by a
Winterstein approximation).

Original language | English |
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Title of host publication | Probabilistic mechanics & structural reliability : Proceedings of the Seventh Specialty Conference |

Place of Publication | new york |

Publisher | American Society of Civil Engineers |

Publication date | 1996 |

Pages | 254-257 |

ISBN (Print) | 0-7844-0184-5 |

Publication status | Published - 1996 |

Event | 7th Specialty Conference on Probabilistic Mechanics and
Structural Reliability - Worchester , Massachusetts, USA Duration: 1 Jan 1996 → … |

### Conference

Conference | 7th Specialty Conference on Probabilistic Mechanics and Structural Reliability |
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City | Worchester , Massachusetts, USA |

Period | 01/01/1996 → … |

## Cite this

Mohr, G. (1996). Higher Moments of Weighted Integrals of Non-Gaussian Fields. In

*Probabilistic mechanics & structural reliability: Proceedings of the Seventh Specialty Conference*(pp. 254-257). American Society of Civil Engineers.