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Characterization of the skew-normal distribution. (English) Zbl 1056.62014

Summary: Two characterization results for the skew-normal distribution based on quadratic statistics have been obtained. The results specialize to known characterizations of the standard normal distribution and generalize to the characterizations of members of a larger family of distributions. Results on the decomposition of the family of distributions of random variables whose square is distributed as \(\chi_1^2\) are obtained.

MSC:

62E10 Characterization and structure theory of statistical distributions
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