A new class of skew-symmetric distributions and related families |
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| Authors: | Héctor W. Gómez Héctor Varela Ignacio Vidal |
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| Affiliation: | 1. Departamento de Matemáticas, Facultad de Ciencias Básicas , Universidad de Antofagasta , Antofagasta , Chile hgomez@uantof.cl;3. Departamento de Matemáticas, Facultad de Ciencias Básicas , Universidad de Antofagasta , Antofagasta , Chile;4. Instituto de Matemática y Física, Universidad de Talca , Talca , Chile |
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| Abstract: | In this work, we investigate a new class of skew-symmetric distributions, which includes the distributions with the probability density function (pdf) given by g α(x)=2f(x) G(α x), introduced by Azzalini [A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178]. We call this new class as the symmetric-skew-symmetric family and it has the pdf proportional to f(x) G β(α x), where G β(x) is the cumulative distribution function of g β(x). We give some basic properties for the symmetric-skew-symmetric family and study the particular case obtained from the normal distribution. |
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| Keywords: | symmetric-skew-symmetric distribution skew-symmetric distribution skew-normal distribution skew-Cauchy distribution |
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