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.