Representation of non-Gaussian probability distributions in stochastic load-flow studies by the method of Gaussian sum approximations

1983 ◽  
Vol 130 (4) ◽  
pp. 165 ◽  
Author(s):  
H.R. Sirisena ◽  
E.P.M. Brown
Keyword(s):  
Probability Distributions ◽  
Load Flow ◽  
Gaussian Sum ◽  
Stochastic Load ◽  
Non Gaussian

Non-Gaussian probability distributions of solar wind fluctuations

1994 ◽  
Vol 12 (12) ◽  
pp. 1127-1138 ◽  
Author(s):  
E. Marsch ◽  
C. Y. Tu
Keyword(s):  
Solar Wind ◽  
Probability Distributions ◽  
Time Lag ◽  
Small Scale ◽  
Time Lags ◽  
Mhd Turbulence ◽  
Theoretical Concepts ◽  
Fluid Turbulence ◽  
Long Time ◽  
Non Gaussian

Abstract. The probability distributions of field differences ∆x(τ)=x(t+τ)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag τ, ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of ∆x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale τ by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of ∆x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.

Non-Gaussian probability distributions for a vortex fluid

1977 ◽  
Vol 20 (3) ◽  
pp. 356 ◽  
Author(s):  
T. S. Lundgren ◽  
Y. B. Pointin
Keyword(s):  
Probability Distributions ◽  
Non Gaussian

scholarly journals Heavy-tailed random matrices

2018 ◽  
Author(s):  
Vladimir Kravtsov
Keyword(s):  
Random Matrices ◽  
Heavy Tails ◽  
Probability Distributions ◽  
Basin Of Attraction ◽  
Random Variables ◽  
Universal Properties ◽  
Random Matrix Ensembles ◽  
Free Random Variables ◽  
Heavy Tailed ◽  
Non Gaussian

This article considers non-Gaussian random matrices consisting of random variables with heavy-tailed probability distributions. In probability theory heavy tails of distributions describe rare but violent events which usually have a dominant influence on the statistics. Furthermore, they completely change the universal properties of eigenvalues and eigenvectors of random matrices. This article focuses on the universal macroscopic properties of Wigner matrices belonging to the Lévy basin of attraction, matrices representing stable free random variables, and a class of heavy-tailed matrices obtained by parametric deformations of standard ensembles. It first examines the properties of heavy-tailed symmetric matrices known as Wigner–Lévy matrices before discussing free random variables and free Lévy matrices as well as heavy-tailed deformations. In particular, it describes random matrix ensembles obtained from standard ensembles by a reweighting of the probability measure. It also analyses several matrix models belonging to heavy-tailed random matrices and presents methods for integrating them.

scholarly journals Need for Caution in Interpreting Extreme Weather Statistics

2015 ◽  
Vol 28 (23) ◽  
pp. 9166-9187 ◽  
Author(s):  
Prashant D. Sardeshmukh ◽  
Gilbert P. Compo ◽  
Cécile Penland
Keyword(s):  
Process Model ◽  
Large Scale ◽  
Probability Distributions ◽  
Extreme Weather ◽  
Recent Change ◽  
Atmospheric Variability ◽  
Tail Probabilities ◽  
The North ◽  
Special Cases ◽  
Non Gaussian

Abstract Given the reality of anthropogenic global warming, it is tempting to seek an anthropogenic component in any recent change in the statistics of extreme weather. This paper cautions that such efforts may, however, lead to wrong conclusions if the distinctively skewed and heavy-tailed aspects of the probability distributions of daily weather anomalies are ignored or misrepresented. Departures of several standard deviations from the mean, although rare, are far more common in such a distinctively non-Gaussian world than they are in a Gaussian world. This further complicates the problem of detecting changes in tail probabilities from historical records of limited length and accuracy. A possible solution is to exploit the fact that the salient non-Gaussian features of the observed distributions are captured by so-called stochastically generated skewed (SGS) distributions that include Gaussian distributions as special cases. SGS distributions are associated with damped linear Markov processes perturbed by asymmetric stochastic noise and as such represent the simplest physically based prototypes of the observed distributions. The tails of SGS distributions can also be directly linked to generalized extreme value (GEV) and generalized Pareto (GP) distributions. The Markov process model can be used to provide rigorous confidence intervals and to investigate temporal persistence statistics. The procedure is illustrated for assessing changes in the observed distributions of daily wintertime indices of large-scale atmospheric variability in the North Atlantic and North Pacific sectors over the period 1872–2011. No significant changes in these indices are found from the first to the second half of the period.

Convolution PHD Filtering for Nonlinear Non-Gaussian Models

2011 ◽  
Vol 213 ◽  
pp. 344-348
Author(s):  
Jian Jun Yin ◽  
Jian Qiu Zhang
Keyword(s):  
Parallel Implementation ◽  
Gaussian Mixture ◽  
Probability Hypothesis Density ◽  
Gaussian Sum ◽  
Multi Target Tracking ◽  
Lower Complexity ◽  
Observation Noise ◽  
Non Gaussian ◽  
Convolution Filters ◽  
Cphd Filter

A novel probability hypothesis density (PHD) filter, called the Gaussian mixture convolution PHD (GMCPHD) filter was proposed. The PHD within the filter is approximated by a Gaussian sum, as in the Gaussian mixture PHD (GMPHD) filter, but the model may be non-Gaussian and nonlinear. This is implemented by a bank of convolution filters with Gaussian approximations to the predicted and posterior densities. The analysis results show the lower complexity, more amenable for parallel implementation of the GMCPHD filter than the convolution PHD (CPHD) filter and the ability to deal with complex observation model, small observation noise and non-Gaussian noise of the proposed filter over the existing Gaussian mixture particle PHD (GMPPHD) filter. The multi-target tracking simulation results verify the effectiveness of the proposed method.

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