Characterization of Distributions Based on Certain Powers of Random Variables

Wen-Jang Huang ； Yen-Ning Huang ； Chia-Ling Lai

《中國統計學報》 43卷4期 (2005/12) Pp. 423-432

https://doi.org/10.29973/JCSA.200512.0004

並列摘要

It is well known that if W is N(0, 1) distributed, then W^2 has the X(superscript 2 subscript 1) distribution. Roberts and Geisser(1966) generalized this result and gave a necessary and sufficient condition for the square of a random variable to be gamma distributed. In this note, first the class of random variables is characterized when the distribution of its nth power is given, where n is a positive integer. Next, some characterization results based on certain quadratic statistics are also provided.

並列關鍵字

Characterization ； exponential family

參考文獻

Arellano-Valle, R.B.,Gómez, H.W.,Quintana, F.A.(2003).A new class of skew-normal distributions.Communications in Statistics-Theory and Methods.33,1465-1480.

Azzalini, A.(1985).A class of distributions which includes the normal ones.Scandinavian Journal of Statistics.12,171-178.

Gupta, A.K.,Nguyen, T.T.,Sanqui, J.A.T.(2004).Characterization of the skew-normal distribution.Annals of the Institute of Statistical Mathematics.56,351-360.

Robers, C.(1971).On the distribution of random variables whose mth absolute power is gamma.Sankhy? Series A.33,229-232.

Robers, C.,Geisser, S.(1966).A necessary and sufficient condition for the square of a random variable to be gamma.Biometrika.53,275-278.