Moments of scale mixtures of skew-normal distributions and their quadratic forms

Hyoung-Moon Kim and Chiwhan Kim

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 3, 1117-1126

Abstract: We obtain the first four moments of scale mixtures of skew-normal distributions allowing for scale parameters. The first two moments of their quadratic forms are obtained using those moments. Previous studies derived the moments, but all relevant results do not allow for scale parameters. In particular, it is shown that the mean squared error becomes an unbiased estimator of σ2 with skewed and heavy-tailed errors. Two measures of multivariate skewness are calculated.

Date: 2017
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DOI: 10.1080/03610926.2015.1011339

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