I have a Chi-squared RV with 2NL degrees of freedom and I am interested in the distribution of its square ($Y=X^2$). I have tried the transformation method to get the expression for the pdf of Y as:
$f_Y(y)=\frac{1}{2^{NL+1} \Gamma(NL)} y^{NL / 2-1} e^{-\sqrt{y} / 2}$
I am not sure about the type of RV that corresponds to this pdf. Is this some standard type of known distribution? Thanks!