# Rotation invariant distributions

• Wlodzimierz Bryc
Chapter
Part of the Lecture Notes in Statistics book series (LNS, volume 100)

## 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 1 2 + a 2 2 + … + a 2 n =1.

## Keywords

Characteristic Function Unit Sphere Infinite Sequence Symmetric Sequence Real Period
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.