Characterization of Distributions Based on Certain Powers of Random Variables

10.29973/JCSA.200512.0004

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

Characterization ； exponential family

中國統計學報

43卷4期（2005 / 12 / 01）

423 - 432

英文

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.

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