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On the Multivariate Normal Hazard

✍ Scribed by Pushpa L. Gupta; Ramesh C. Gupta

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 247 KB
Volume: 62
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1997.1675

No coin nor oath required. For personal study only.

✦ Synopsis

It is well known that the hazard rate of a univariate normal distribution is increasing. In this paper, we prove that the hazard gradient, in the case of general multivariate normal distribution, is increasing in the sense of Johnson and Kotz.

1997 Academic Press 1. Definition 1. The joint multivariate hazard rate of m jointly absolutely continuous random variables X 1 , X 2 , ..., X m is defined as the vector

where G(x)=P(X i >x i , i=1, 2, ..., m) is the joint survival function. For convenience, we shall write &( Â x j ) ln G(x)=h j (x). Note that h j (x) is the article no. MV971675 64 0047-259XÂ97 25.00

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