On some characterisations of the normal law

Radhakrishna Rao, C. (1967) On some characterisations of the normal law Sankhya - Series A, 29 . pp. 1-14. ISSN 0581-572X

Full text not available from this repository.

Official URL: http://sankhya.isical.ac.in/search/29a1/29a1001.ht...


Let X1,...,Xn be independent variables and Y1,...,Yn be linear functions of X1,...,Xn. In this paper, the conditions under which the equations E(Yi|Yp+1,...,Yp+j)=0,i=1,..,p imply normality of X1,...,Xn are examined. An important case considered is when E(Y1|Y2)=0 involving only two linear functions (with p=1, j=0), which provides a generalisation of the earlier results on the characterisation of the normal law by Darmois, Kagan, Linnik, Rao, Skitovich and others. The conditions imposed to ensure normality are of two types, one on the nature of the coefficients in the linear functions Yi and another on the nature of the distributions of X1,...,Xn, such as identical distribution, existence of moments etc.

Item Type:Article
Source:Copyright of this article belongs to Indian Statistical Institute.
ID Code:54737
Deposited On:12 Aug 2011 13:00
Last Modified:12 Aug 2011 13:00

Repository Staff Only: item control page