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Scalability Properties of the S‐Distribution
Author(s) -
Voit Eberhard O.,
Schwacke Lorelei H.
Publication year - 1998
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/(sici)1521-4036(199810)40:6<665::aid-bimj665>3.0.co;2-g
Subject(s) - mathematics , skewness , distribution (mathematics) , combinatorics , quantile , statistics , mathematical analysis
Previous work has shown that the S‐distribution is a valuable tool for data analysis and for the classification of continuous and discrete distribution functions. The distribution has four parameters: one determines its location, one is related to the variance, and two control its shape. The distributional structure allows symmetry as well as skewness to the right or the left. This offers great flexibility and, among other analyses, facilitates the simultaneous investigation of random variables whose distributions differ in shape. The present paper demonstrates that mean, variance, and quantiles of any S‐distribution can be computed with simple algebraic operations from corresponding properties of a standard S‐distribution , sSd , which is characterized by only the two shape parameters. This scalability is comparable with the use of z‐scores when dealing with normal distributions.