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On Characterizing the Multivariate Linear Exponential Distribution1

Published online by Cambridge University Press:  20 November 2018

D. G. Kabe
D. G. Kabe*
Affiliation:
St. Mary's University, Halifax 572
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If x and y are independent p component column vectors, and the conditional distribution of x, given x+y = z, is known, what can be said about the distributions of x and y? This problem has been solved by Seshadri (1966) in the particular case when the conditional distribution of x, given x+y = z, is multivariate normal. In fact Seshadri′s paper implicitly contains a characterization of the multivariate linear exponential distribution

(1)

where A(x) is a function of x not involving the p component column vector w of constant terms.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969, pp. 567 - 572
Copyright
Copyright © Canadian Mathematical Society 1969

Footnotes

1

This research work was done while the author held a summer (1967) research fellowship of the Canadian Mathematical Congress.

References

1. Aczel, J., Lectures on functional equations and their applications. (Academic Press, New York, 1965).Google Scholar
2. Mathai, A.M., On the structural properties of the conditional distributions. Canad. Math. Bull. 10 (1967) 239–245.Google Scholar
3. Seshadri, V., A characteristic property of the multi-variate normal distribution. Ann. Math. Statist. 37 (1966) 1829–1831.Google Scholar