Related papers: Skewness and kurtosis analysis for non-Gaussian di…
Skewness and kurtosis are fundamental statistical moments commonly used to quantify asymmetry and tail behavior in probability distributions. Despite their widespread application in statistical mechanics, condensed matter physics, and…
An attractive and simple hypothesis for the formation of large-scale structure is that it developed by gravitational instability from primordial fluctuations with an initially Gaussian probability distribution. Non-linear gravitational…
The impact of the third (skewness) and fourth (kurtosis) reduced centered moments on the statistical modeling of E1 lines in complex atomic spectra is investigated through the use of Gram-Charlier, Normal Inverse Gaussian and Generalized…
In this paper, I present the calculation of the third and fourth moments of both the distribution function of the large--scale density and the large--scale divergence of the velocity field, $\theta$. These calculations are made by the mean…
The non-Gaussian measures of the particle number fluctuations -- skewness $S\sigma$ and kurtosis $\kappa \sigma^2$ -- are calculated in a vicinity of the critical point. This point corresponds to the end point of the first-order liquid-gas…
Noise is an unavoidable part of most measurements which can hinder a correct interpretation of the data. Uncertainties propagate in the data analysis and can lead to biased results even in basic descriptive statistics such as the central…
Using a discrete wavelet based space-scale decomposition (SSD), the spectrum of the skewness and kurtosis is developed to describe the non-Gaussian signatures in cosmologically interesting samples. Because the basis of the discrete wavelet…
We investigate the impact of non-Gaussian scatter in the cluster mass-observable scaling relation on the mass and redshift distribution of clusters detected by wide area surveys. We parameterize non-Gaussian scatter by incorporating the…
In this paper, we propose that relations between high order moments of data distributions, for example between the skewness (S) and kurtosis (K), allow to point to theoretical models with understandable structural parameters. The…
Central moments and cumulants are often employed to characterize the distribution of data. The skewness and kurtosis are particularly useful for the detection of outliers, the assessment of departures from normally distributed data,…
Kurtosis is seen as a measure of the discrepancy between the observed data and a Gaussian distribution and is defined when the 4th moment is finite. In this work an empirical study is conducted to investigate the behaviour of the sample…
We calculate the kurtosis of a large-scale density field which has undergone weakly non-linear gravitational evolution from arbitrary non-Gaussian initial conditions. It is well known that the weakly evolved {\twelveit skewness} is equal to…
The thermodynamic uncertainty relation is a prominent result in stochastic thermodynamics that provides a bound on the fluctuations of any thermodynamic flux, also known as current, in terms of the average rate of entropy production. Such…
We explore the possibility of putting constraints on dark energy models with statistical property of large scale structure in the non-linear region. In particular, we investigate the $w$ dependence of non-Gaussianity of the smoothed density…
The concept of kurtosis is used to describe and compare theoretical and empirical distributions in a multitude of applications. In this connection, it is commonly applied to asymmetric distributions. However, there is no rigorous…
Kurtosis minus squared skewness is bounded from below by 1, but for unimodal distributions this parameter is bounded by 189/125. In some applications it is natural to compare distributions by comparing their kurtosis-minus-squared-skewness…
The Mardia measures of multivariate skewness and kurtosis summarize the respective characteristics of a multivariate distribution with two numbers. However, these measures do not reflect the sub-dimensional features of the distribution.…
We discuss the non--linear growth of the excess kurtosis parameter of the smoothed density fluctuation field $\delta$, $S_4\equiv[\lan\delta^{\,4}\ran-3\lan\delta^{\,2}\ran^2]/ \lan\delta^{\,2}\ran^3$ in an Einstein--de Sitter universe. We…
Skewness and non-Gaussian behavior are essential features of the distribution of short-scale velocity increments in isotropic turbulent flows. Yet, although the skewness has been generally linked to time-reversal symmetry breaking and…
The generalized extreme value distribution and its particular case, the Gumbel extreme value distribution, are widely applied for extreme value analysis. The Gumbel distribution has certain drawbacks because it is a non-heavy-tailed…