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Characterization of matrix probability distributions by mean residual lifetime

Published online by Cambridge University Press:  24 October 2008

P. E. Jupp
P. E. Jupp
Affiliation:
Department of Statistics, University of St Andrews
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Extract

The mean residual lifetime of a real-valued random variable X is the function e defined by

One of the more important properties of the mean residual lifetime function is that it determines the distribution of X. See, for example, Swartz [10]. References to related characterizations are given by Galambos and Kotz [3], pages 30–35. It was established by Jupp and Mardia[6] that this property holds also for vector-valued X. As (1·1) makes sense if X is a random symmetric matrix, it is natural to ask whether the property holds in this case also. The purpose of this note is to show that, under certain regularity conditions, the distributions of such matrices are indeed determined by their mean residual lifetimes.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 3 , November 1986 , pp. 583 - 589
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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