Rotation invariant distributions

Abstract

Definition 4.1.1 A random vector X = (X₁, X₂,…, X _n ) is spherically symmetric if the distribution of every linear form

$${a_1}{X_1} + {a_2}{X_2} + \ldots + {a_n}{X_n} \cong {X_1}$$

((4.1))

is the same for all a₁, ,a₂, …,a _n ,provideda ²₁ + a ²₂ + … + a ⁿ₂ =1.