### Abstract

Positive random fields with known marginal properties and known
correlation function are not numerous in the literature. The most
prominent example is the log\-normal field for which the complete
distribution is known and for which the reciprocal field is also
lognormal. It is of interest to supplement the catalogue of
positive fields beyond the class of those obtained by simple
marginal transformation of a Gaussian field, this class containing
the lognormal field.As a minimum for a random field to be included
in the catalogue itis required that an algorithm for simulation of
realizations can be constructed and that the one-dimensional
marginal moments up to at least the fourth order as well as the
correlation function of the field are given explicitly. This
information makes it possible to use and check the so-called
Winterstein approximations for finite element calculations of
structures with material properties modeled in terms of the
considered random fields.The paper addsthe gamma field, the Fisher
field, the beta field, and their reciprocal fields to the
catalogue. These fields are all defined on the basis of sums of
squares of independent standard Gaussian random variables.All the
existing marginal moments and the correlation functions are
obtained explicitly. Also an inverse Gaussian fieldis added to the
catalogue. It is defined in terms of first passage times in
correlated joint Brownian motions. Finally an n-dimensional random
vector of positive components is defined such that it can be used
as an approximation to a discretization of a homogeneous Gaussian
field with any specified correlation function and coefficient of
variation less than 1/(square root of n).

Original language | English |
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Title of host publication | Structural Safety and Reliability |

Place of Publication | Rotterdam |

Publisher | CRC Press/Balkema |

Publication date | 1998 |

Pages | 723-730 |

Publication status | Published - 1998 |

Event | 7th International Conference on Structural Safety and Reliability - Kyoto, Japan Duration: 24 Nov 1997 → 28 Nov 1997 Conference number: 7 |

### Conference

Conference | 7th International Conference on Structural Safety and Reliability |
---|---|

Number | 7 |

Country | Japan |

City | Kyoto |

Period | 24/11/1997 → 28/11/1997 |

## Cite this

Hasofer, A. M., Ditlevsen, O. D., & Tarp-Johansen, N. J. (1998). Positive random fields for modeling material stiffness and
compliance. In

*Structural Safety and Reliability*(pp. 723-730). CRC Press/Balkema.