Sankhya: The Indian Journal of Statistics

2004, Volume 66, Pt. 4, 593--606

Characterizations of the Skew-normal and Generalized Chi Distributions

By

Barry C. Arnold, University of California, Riverside, USA
Gwo Dong Lin, Academia Sinica, Taipei, Taiwan

SUMMARY. We point out that the skew-normal distributions and their limits are exactly the distributions of order statistics of bivariate normally  distributed variables.  The moment problem of powers of skew-normal random variables is investigated.  Using generalized skew-normal distributions we are able to characterize the distributions of random variables whose squares obey the chi-square distribution with one degree of freedom. Finally, we solve a general distribution equation by utilizing the concept of a skew-symmetric function.

AMS (1991) subject classification}. Primary 60E05, 62E10, 62G30 ;.

Key words and phrases. Skew-normal distribution, generalized chi distribution, order statistics, moment problem, distribution equation.

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