Rotation invariant distributions

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


Definition 4.1.1 A random vector X = (X1, X2,…, X n ) is spherically symmetric if the distribution of every linear form
$${a_1}{X_1} + {a_2}{X_2} + \ldots + {a_n}{X_n} \cong {X_1}$$
is the same for all a1, ,a2, …,a n ,provideda 1 2 + a 2 2 + … + a 2 n =1.


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.


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Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Wlodzimierz Bryc
    • 1
  1. 1.Department of MathematicsUniversity of CincinnatiCincinnatiUSA

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