For most but not all non-Gaussian random variables the Kurtosis is non-zero.
So the Kurtosis can also be positive or negative.
Typically, then the non-Gaussianity is measured as the absolute value of the Kurtosis or the Kurtosis to the power of two..
Introduction.
Non-Gaussian distribution refers to a class of probability distributions that deviate from the symmetric and bell-shaped pattern of the Gaussian distribution (also known as the normal distribution)..
Non-Gaussian distribution refers to a class of probability distributions that deviate from the symmetric and bell-shaped pattern of the Gaussian distribution (also known as the normal distribution)..
The non-Gaussian parameter has been interpreted in terms of dynamical hetero- geneity due to different local environments.
It was found that the non-Gaussian parameter A increases with decreasing temperature and with decreasing the fragility index m, especially below T g..
Article Talk.
In physics, a non-Gaussianity is the correction that modifies the expected Gaussian function estimate for the measurement of a physical quantity.
In physical cosmology, the fluctuations of the cosmic microwave background are known to be approximately Gaussian, both theoretically as well as experimentally..
κ 4 ( z ) = E [ z 4 ] − 3 ( E [ z 2 ] ) 2 , is known as the kurtosis of the variable and it is a measure of non-Gaussianity.
Variables following the Gaussian distribution have zero kurtosis..
ICA uses the idea of non-Gaussianity to uncover independent components.
Non-Gaussianity quantifies how far the distribution of a random variable is from being Gaussian.
Example measures of non-Gaussianity are kurtosis and negentropy.
Why such a measure is helpful follows from the Central Limit Theorem..
Since non-Gaussianity directly probes the dynamics in the early Universe, a detection would present a monumental discovery in cosmology, providing clues about physics at energy scales as high as the GUT scale. 5 pages + references; Submitted to the Astro2020 call for science white papers.
This version:
In physical cosmology, the fluctuations of the cosmic microwave background are known to be approximately Gaussian, both theoretically as well as experimentally.
However, most theories predict some level of non-Gaussianity in the primordial density field.
Most inflationary models of the early Universe predict that the initial density fluctuations in the Universe giving rise to the temperature-fluctuations in the Cosmic Microwave Background (CMB) and in the Large Scale Structure (LSS) are nearly Gaussian distributed.
In physics, a non-Gaussianity is the correction that modifies the expected Gaussian function estimate for the measurement of a physical quantity .
In physical cosmology, the fluctuations of the cosmic microwave background are known to be approximately Gaussian, both theoretically as well as experimentally.
