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Moments of scale mixtures of skew-normal distributions and their quadratic forms. (English) Zbl 1364.62119

Summary: 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 \(\sigma^2\) with skewed and heavy-tailed errors. Two measures of multivariate skewness are calculated.

MSC:

62H10 Multivariate distribution of statistics
62E15 Exact distribution theory in statistics

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