## The Annals of Mathematical Statistics

### A Characterization of Normality

M. V. Tamhankar

#### Abstract

A probability distribution on an $n$-dimensional Euclidean space can be specified by giving either the joint distribution of the usual rectangular coordinates or by the joint distribution of the polar coordinates. The object of this note is to obtain a characterization of normality in terms of independence of these coordinates under suitable regularity conditions. Further, if we slightly relax these conditions we get a new class of distributions which includes the normal distribution.

#### Article information

Source
Ann. Math. Statist., Volume 38, Number 6 (1967), 1924-1927.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177698630

Digital Object Identifier
doi:10.1214/aoms/1177698630

Mathematical Reviews number (MathSciNet)
MR219114

Zentralblatt MATH identifier
0157.48703

JSTOR