A remark on the criterion of continuity of Gaussian sample function

Wind pressure fluctuations acting on space structures are important for prediction of peak pressure values and for fatigue design purpose. Collection of several time histories of pressure fluctuations by traditional wind tunnel measurements is time consuming and expensive. Thus, a study on developing new wind pressure simulation technique on domed structures is carried out. An efficient, flexible and easily applied stochastic non-Gaussian simulation algorithm is presented using a cumulative distribution function (CDF) mapping technique that converges to a desired target power spectral density. This method first generates Gaussian sample fields using wavelet bases and then maps them into non-Gaussian sample fields with the aid of an iterative procedure. Results from this technique are presented and compared with those from the wind tunnel experiments. The advantages and limitations of this method are also discussed.

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The horizon problem for random surfaces

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410006967x ◽

1991 ◽

Vol 109 (1) ◽

pp. 211-219 ◽

Cited By ~ 3

Author(s):

K. J. Falconer

Keyword(s):

Computer Simulation ◽

Stochastic Processes ◽

Random Field ◽

Random Fields ◽

Sample Function ◽

Gaussian Fields ◽

Random Surfaces ◽

Horizon Problem ◽

Typical Sample

Computer simulation of landscapes and skylines has recently attracted a great deal of interest: see [6, 7]. Specification of a ‘landscape’ requires a function f: D → ℝ on a subset D of ℝ2, selected so that the apparent irregularity and randomness of the surface {(t,f(t)): t ∈ D} corresponds to what might be observed in nature. It is natural to look to random fields (that is, stochastic processes in two variables), and in particular to Gaussian fields, for functions with such properties. Even when an appropriate random field has been selected, determination of a typical sample function is far from easy [7].

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Exact distributions of order statistics from ln,p-symmetric sample distributions

Dependence Modeling ◽

10.1515/demo-2017-0013 ◽

2017 ◽

Vol 5 (1) ◽

pp. 221-245 ◽

Cited By ~ 1

Author(s):

K. Müller ◽

W.-D. Richter

Keyword(s):

Distribution Function ◽

Finite Number ◽

Order Statistics ◽

Cumulative Distribution Function ◽

Cumulative Distribution ◽

Symmetric Distributions ◽

Sample Distribution ◽

Special Cases ◽

Exact Distributions ◽

Gaussian Sample

Abstract We derive the exact distributions of order statistics from a finite number of, in general, dependent random variables following a joint ln,p-symmetric distribution. To this end,we first review the special cases of order statistics fromspherical aswell as from p-generalized Gaussian sample distributions from the literature. To study the case of general ln,p-dependence, we use both single-out and cone decompositions of the events in the sample space that correspond to the cumulative distribution function of the kth order statistic if they are measured by the ln,p-symmetric probability measure.We show that in each case distributions of the order statistics from ln,p-symmetric sample distribution can be represented as mixtures of skewed ln−ν,p-symmetric distributions, ν ∈ {1, . . . , n − 1}.

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