On the multivariate normal hazard
type: Item
instance of: scholarly article
title: On the multivariate normal hazard
zbMATH Open document ID: 0895.60021
author: Pushpa L. Gupta
author: Ramesh C. Gupta
published in: Journal of Multivariate Analysis
publication date: 1997-09-04T00:00:00Z
review text: It is well known that the hazard rate of a univariate normal distribution is increasing. \textit{N. L. Johnson} and \textit{S. Kotz} [ibid. 5, 53-66 (1975; Zbl 0297.60013)] presented a vector definition of multivariate hazard rates and associated definitions of increasing and decreasing multivariate distributions. They showed that in a bivariate normal case, the bivariate hazard is increasing provided that the correlation coefficient is positive. We first show that in the bivariate normal case, the hazard rate is increasing without the condition on the correlation coefficient imposed by Johnson and Kotz. The result is then extended to the trivariate normal case and finally to the general \(m\)-dimensional multivariate case.
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 1057403
zbMATH Keywords: univariate normal distribution
zbMATH Keywords: multivariate distributions
zbMATH Keywords: correlation coefficient
MaRDI profile type: Publication
full work available at URL: jmva.1997.1675
OpenAlex ID: W2007992358
cites work: Bathtub and Related Failure Rate Characterizations
cites work: A vector multivariate hazard rate
cites work: Some comments on the hazard gradient
cites work: Q3219581
DOI: 10.1006/JMVA.1997.1675
description: scientific article; zbMATH DE number 1057403