Abstract
This paper describes a complementary tool for fitting probabilistic distributions in data analysis. First, we examine the well known bivariate index of skewness and the aggregate skewness function, and then introduce orderings of the skewness of probability distributions. Using an example, we highlight the advantages of this approach and then present results for these orderings in common uniparametric families of continuous distributions, showing that the orderings are well suited to the intuitive conception of skewness and, moreover, that the skewness can be controlled via the parameter values.
Highlights
IntroductionDetailed knowledge of the characteristics of probability models is desirable (if not essential) if data are to be modeled properly
Detailed knowledge of the characteristics of probability models is desirable if data are to be modeled properly
Many studies have been conducted in this area, and the following are significant: Lehmann (1955) [2], which is of seminal importance; Arnold (1987) [3], who compared random variables according to stochastic ordering in a particular
Summary
Detailed knowledge of the characteristics of probability models is desirable (if not essential) if data are to be modeled properly. We extend the tool-box approach to fit data from probability distributions, introducing two orderings that are deduced from the skewness measures given in [15]. The first of those orderings is based on the positive part of the bivariate index of skewness, which in many instances coincides with the well known γ M ( F ).
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