Norms of Gaussian sample functions

1976 ◽  
pp. 20-41 ◽  
Author(s):  
B. S. Cirel'son ◽  
I. A. Ibragimov ◽  
V. N. Sudakov
Keyword(s):  
Gaussian Sample

scholarly journals A Note on the Absence of Tangencies in Gaussian Sample Paths

1968 ◽  
Vol 39 (1) ◽  
pp. 261-262 ◽  
Author(s):  
Donald Ylvisaker
Keyword(s):  
Sample Paths ◽  
Gaussian Sample

Simulation of Non-Gaussian Wind Pressure Fields on Domed Structures

2010 ◽  
Vol 163-167 ◽  
pp. 4142-4148
Author(s):  
Nyi Nyi Aung ◽  
Ji Hong Ye
Keyword(s):  
Wind Tunnel ◽  
Pressure Fluctuations ◽  
Wind Pressure ◽  
Cumulative Distribution ◽  
Mapping Technique ◽  
Power Spectral ◽  
Time Histories ◽  
Gaussian Simulation ◽  
Gaussian Sample ◽  
Non Gaussian

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.

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

2017 ◽  
Vol 5 (1) ◽  
pp. 221-245 ◽  
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}.

Generating a Gaussian sample

1956 ◽  
Vol 2 (2) ◽  
pp. 87-90 ◽  
Author(s):  
S. Stein ◽  
J. Storer
Keyword(s):  
Gaussian Sample

The distribution of the convex hull of a Gaussian sample

1980 ◽  
Vol 17 (03) ◽  
pp. 686-695 ◽  
Author(s):  
William F. Eddy
Keyword(s):  
Weak Convergence ◽  
Convex Hull ◽  
Poisson Point Process ◽  
Point Processes ◽  
Convex Sets ◽  
Continuous Mapping ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
Limit Process ◽  
Gaussian Sample

The distribution of the convex hull of a random sample ofd-dimensional variables is described by embedding the collection of convex sets into the space of continuous functions on the unit sphere. Weak convergence of the normalized convex hull of a circular Gaussian sample to a process with extreme-value marginal distributions is demonstrated. The proof shows that an underlying sequence of point processes converges to a Poisson point process and then applies the continuous mapping theorem. Several properties of the limit process are determined.

Efficient Gaussian sample specific network marker discovery and drug enrichment analysis validation

2019 ◽  
Vol 83 ◽  
pp. 107139
Author(s):  
Wenbin Liu ◽  
Yugai Du ◽  
Gang Fang ◽  
Zheng Kou ◽  
Xianghong Wang ◽  
...  
Keyword(s):  
Enrichment Analysis ◽  
Gaussian Sample ◽  
Marker Discovery

scholarly journals Mock galaxy shape catalogues in the Subaru Hyper Suprime-Cam Survey

2019 ◽  
Vol 486 (1) ◽  
pp. 52-69 ◽  
Author(s):  
Masato Shirasaki ◽  
Takashi Hamana ◽  
Masahiro Takada ◽  
Ryuichi Takahashi ◽  
Hironao Miyatake
Keyword(s):  
Measurement Errors ◽  
Degrees Of Freedom ◽  
Likelihood Function ◽  
Analytical Formula ◽  
Real Data ◽  
Chi Square ◽  
Photometric Redshift ◽  
Cent Level ◽  
Cosmic Shear ◽  
Gaussian Sample

Abstract We use the full-sky ray-tracing weak lensing simulations to generate 2268 mock catalogues for the Subaru Hyper Suprime-Cam (HSC) survey first-year shear catalogue. Our mock catalogues take into account various effects as in the real data: the survey footprints, inhomogeneous angular distribution of source galaxies, statistical uncertainties in photometric redshift (photo-z) estimate, variations in the lensing weight, and the statistical noise in galaxy shape measurements including both intrinsic shapes and the measurement errors. We then utilize our mock catalogues to evaluate statistical uncertainties expected in measurements of cosmic shear two-point correlations ξ± with tomographic redshift information for the HSC survey. We develop a quasi-analytical formula for the Gaussian sample variance properly taking into account the number of source pairs in the survey footprints. The standard Gaussian formula significantly overestimates or underestimates the mock results by 50 per cent level. We also show that different photo-z catalogues or the six disconnected fields, rather than a consecutive geometry, cause variations in the covariance by ${\sim } 5{{\ \rm per\ cent}}$. The mock catalogues enable us to study the chi-square distribution for ξ±. We find the wider distribution than that naively expected for the distribution with the degrees of freedom of data vector used. Finally, we propose a method to include non-zero multiplicative bias in mock shape catalogue and show that the non-zero multiplicative bias can change the effective shape noise in cosmic shear analyses. Our results suggest an importance of estimating an accurate form of the likelihood function (and therefore the covariance) for robust cosmological parameter inference from the precise measurements.

Non-parametric estimation of reference intervals in small non-Gaussian sample sets

2009 ◽  
Vol 14 (4) ◽  
pp. 185-192 ◽  
Author(s):  
Johan Bjerner ◽  
Elvar Theodorsson ◽  
Eivind Hovig ◽  
Anders Kallner
Keyword(s):  
Reference Intervals ◽  
Parametric Estimation ◽  
Gaussian Sample ◽  
Non Gaussian ◽  
Non Parametric Estimation ◽  
Non Parametric
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