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Flexible Class of Skew‐Symmetric Distributions
Author(s) -
Ma Yanyuan,
Genton Marc G.
Publication year - 2004
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2004.03_007.x
Subject(s) - mathematics , skewness , skew , probability density function , class (philosophy) , probability distribution , symmetric probability distribution , function (biology) , set (abstract data type) , distribution (mathematics) , product (mathematics) , statistical physics , combinatorics , mathematical analysis , statistics , computer science , artificial intelligence , geometry , telecommunications , physics , evolutionary biology , biology , programming language
. We propose a flexible class of skew‐symmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family of distributions, which can capture skewness, heavy tails and multimodality systematically. We present three illustrative examples for the fibreglass data, the simulated data from a mixture of two normal distributions and the Swiss bills data.