New methods are being presented for statistical treatment of different random variables with unknown probability distributions. These include analysis based on the probability circles, probability ellipses, generalized mean values, generalized Pearson correlation coefficient and the beta-function analysis. Unlike other conventional statistical procedures, the main distinctive feature of these new methods is that no assumptions are made about the nature of the probability distribution of the random series being evaluated. Furthermore, the suggested procedures do not introduce uncontrollable errors during their application. The effectiveness of these methods is demonstrated on simulated data with extended and reduced sample sizes having different probability distributions.
Al Shami, Munther R.; Mugdadi, A. R.; Nigmatullin, R. R.; and Osokin, S. I.
Application of Fractional Moments for Comparing Random Variables with Varying Probability Distributions,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
2, Article 3.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss2/3