Remarks for the singular multivariate skew-normal distribution and its quadratic forms. (English) Zbl 1396.60022
Summary: Under the singular multivariate skew normal (SMSN) setting, we showed that, in this paper, the necessary and sufficient conditions for independence of two sub-vectors given in [P. D. Young et al., Stat. Probab. Lett. 122, 58–62 (2017; Zbl 1463.62021)] are equivalent to the results in [the third author et al., J. Multivariate Anal. 100, No. 3, 533–545 (2009; Zbl 1154.62342)]. In addition, the distribution of quadratic form of SMSN random vector is derived, with this new definition of the noncentral skew chi-square distribution. Several examples are given to illustrate our main results.
Keywords:
multivariate skew normal distribution; independent sub vectors; moment generating function; noncentral skew chi square distributionReferences:
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