Characterization ofp-Generalized Normality

In this paper some characterization results ofLp-norm spherical distributions are obtained. It is proved that ifX=(X1, …, Xn)′ has aLp-norm spherical distribution having certain independence properties, thenX1, X2, …, Xnmust be i.i.d. with p.d.f.p(x)∝e−|x|p/c. Also, the largest characterization ofLp-norm spherical distributions is given.