The generalized lambda distribution (GLD) is a flexible four parameter distribution with many practical applications. L-moments of the GLD can be expressed in closed form and are good alternatives for the central moments. The L-moments of the GLD up to an arbitrary order are presented, and a study of L-skewness and L-kurtosis that can be achieved by the GLD is provided. The boundaries of L-skew...

One of the most important problems in time series analysis of stream flow and rainfall data in an area is selecting the best probability distribution. Since the rainfall stations are associated and correlated with each other, so statistical analysis of the station data seamlessly are very important. Therefore, the first step in data analysis, is selecting the prevailing probability distribution...

We derive model independent, non-perturbative supersymmetric sum rules for the magnetic and electric multipole moments of any theory with N = 1 supersymmetry. We find that in any irreducible N = 1 supermultiplet the diagonal matrix elements of the l-multipole moments are completely fixed in terms of their off-diagonal matrix elements and the diagonal (l− 1)-multipole moments. † e-mail: giannak@...

Expressions for (absolute) moments of generalized hyperbolic and normal inverse Gaussian (NIG) laws are given in terms of moments of the corresponding symmetric laws. For the (absolute) moments centred at the location parameter l explicit expressions as series containing Bessel functions are provided. Furthermore, the derivatives of the logarithms of absolute l-centred moments with respect to t...

An important challenge in big data is identification of variables. For this purpose, methods discovering variables with non-standard univariate marginal distributions are proposed. The conventional moments based summary statistics can be well-adopted, but their sensitivity to outliers lead selection on a few rather than distributional shape such as bimodality. To address type non-robustness, th...