Sankhya: The Indian Journal of Statistics
2004, Volume 66, Pt. 4, 593--606
Characterizations of the Skew-normal and Generalized Chi Distributions
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.