Stable non-Gaussian distributions in scientometrics

1985 ◽  
Vol 7 (3-6) ◽  
pp. 459-470 ◽  
Author(s):  
A. I. Yablonsky
Keyword(s):  
Gaussian Distributions ◽  
Non Gaussian

scholarly journals Emergence of skewed non-Gaussian distributions of velocity increments in isotropic turbulence

2019 ◽  
Vol 4 (6) ◽  
Author(s):  
W. Sosa-Correa ◽  
R. M. Pereira ◽  
A. M. S. Macêdo ◽  
E. P. Raposo ◽  
D. S. P. Salazar ◽  
...  
Keyword(s):  
Isotropic Turbulence ◽  
Gaussian Distributions ◽  
Velocity Increments ◽  
Non Gaussian

scholarly journals DETERMINING SOURCE CUMULANTS IN FEMTOSCOPY WITH GRAM–CHARLIER AND EDGEWORTH SERIES

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Momentum Space ◽  
Crucial Role ◽  
Gaussian Distributions ◽  
Edgeworth Series ◽  
The Central Limit Theorem ◽  
Non Gaussian

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

Control charts for non-Gaussian distributions

2007 ◽  
Author(s):  
Florina Babus ◽  
Abdessamad Kobi ◽  
Th. Tiplica ◽  
Ioan Bacivarov ◽  
Angelica Bacivarov
Keyword(s):  
Control Charts ◽  
Gaussian Distributions ◽  
Non Gaussian

Reliability-Based Design Optimization With Confidence Level for Non-Gaussian Distributions Using Bootstrap Method

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Yoojeong Noh ◽  
Kyung K. Choi ◽  
Ikjin Lee ◽  
David Gorsich ◽  
David Lamb
Keyword(s):  
Statistical Model ◽  
Design Optimization ◽  
Confidence Intervals ◽  
Confidence Level ◽  
Bootstrap Method ◽  
Random Variables ◽  
Reliability Based Design Optimization ◽  
Gaussian Distributions ◽  
Reliability Based Design ◽  
Non Gaussian

For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset inaccurate estimation of the input statistical model with Gaussian distributions. For this, the confidence intervals for the mean and standard deviation are calculated using Gaussian distributions of the input random variables. However, if the input random variables are non-Gaussian, use of Gaussian distributions of the input variables will provide inaccurate confidence intervals, and thus yield an undesirable confidence level of the reliability-based optimum design meeting the target reliability βt. In this paper, an RBDO method using a bootstrap method, which accurately calculates the confidence intervals for the input parameters for non-Gaussian distributions, is proposed to obtain a desirable confidence level of the output performance for non-Gaussian distributions. The proposed method is examined by testing a numerical example and M1A1 Abrams tank roadarm problem.

Graphical interpretation of confidence curves in rankit plots

2004 ◽  
Vol 42 (7) ◽  
Author(s):  
Per Hyltoft Petersen ◽  
Ole Blaabjerg ◽  
Marianne Andersen ◽  
Lone G. M. Jørgensen ◽  
Karoline Schousboe ◽  
...  
Keyword(s):  
Reference Values ◽  
Cumulative Frequency ◽  
Normal Curve ◽  
Healthy Individuals ◽  
Gaussian Distributions ◽  
Straight Line ◽  
Kolmogorov Smirnov ◽  
Non Gaussian ◽  
Graphical Presentation ◽  
Smirnov Test

AbstractA well-known transformation from the bell-shaped Gaussian (normal) curve to a straight line in the rankit plot is investigated, and a tool for evaluation of the distribution of reference groups is presented. It is based on the confidence intervals for percentiles of the calculated Gaussian distribution and the percentage of cumulative points exceeding these limits.The process is to rank the reference values and plot the cumulative frequency points in a rankit plot with a logarithmic (ln=logThis is a conservative validation, which is more demanding than the Kolmogorov-Smirnov test. The graphical presentation, however, makes it easy to disclose deviations from ln-Gaussianity, and to make other interpretations of the distributions, e.g., comparison to non-Gaussian distributions in the same plot, where the cumulative frequency percentage can be read from the ordinate. A long list of examples of ln-Gaussian distributions of subgroups of reference values from healthy individuals is presented. In addition, distributions of values from well-defined diseased individuals may showup as ln-Gaussian.It is evident from the examples that the rankit transformation and simple graphical evaluation for non-Gaussianity is a useful tool for the description of sub-groups.

scholarly journals Non-Gaussian Linear Mixing Models for Hyperspectral Images

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Peter Bajorski
Keyword(s):  
Power Distribution ◽  
Error Term ◽  
Hyperspectral Data ◽  
Mixing Models ◽  
Exponential Power Distribution ◽  
Gaussian Distributions ◽  
Independent Components ◽  
Random Behavior ◽  
Exponential Power ◽  
Non Gaussian

Modeling of hyperspectral data with non-Gaussian distributions is gaining popularity in recent years. Such modeling mostly concentrates on attempts to describe a distribution, or its tails, of all image spectra. In this paper, we recognize that the presence of major materials in the image scene is likely to exhibit nonrandomness and only the remaining variability due to noise, or other factors, would exhibit random behavior. Hence, we assume a linear mixing model with a structured background, and we investigate various distributional models for the error term in that model. We propose one model based on the multivariatet-distribution and another one based on independent components following an exponential power distribution. The former model does not perform well in the context of the two images investigated in this paper, one AVIRIS and one HyMap image. On the other hand, the latter model works reasonably well with the AVIRIS image and very well with the HyMap image. This paper provides the tools that researchers can use for verifying a given model to be used with a given image.

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