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A note on scale mixtures of skew normal distribution

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  • Kim, Hyoung-Moon

Abstract

Moments of scale mixtures of skew normal distribution and their quadratic forms are derived using the simple stochastic relationship between skew normal distribution and scale mixtures of skew normal distribution. An application to time series is discussed. It is shown that the mean, covariance, and correlation structure of the sample autocovariance function for a particular class of time series depend on a measure of multivariate kurtosis, but not on a shape parameter. Unlike the multivariate normal distribution and the elliptical distributions with Muirhead kurtosis parameter 0, the covariance and the correlation of the sample autocovariance function for a particular class of time series with underlying scale mixtures of normal distribution are not always negative. We show this using an example of the generalized t distribution. As a by-product, we derived Muirhead kurtosis for some scale mixtures of normal distribution.

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  • Kim, Hyoung-Moon, 2008. "A note on scale mixtures of skew normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1694-1701, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:13:p:1694-1701
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    2. Christian E. Galarza & Tsung-I Lin & Wan-Lun Wang & Víctor H. Lachos, 2021. "On moments of folded and truncated multivariate Student-t distributions based on recurrence relations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 825-850, August.
    3. Jorge M. Arevalillo & Hilario Navarro, 2020. "Data projections by skewness maximization under scale mixtures of skew-normal vectors," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 435-461, June.

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