On the multivariate normal hazard
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.
scientific article; zbMATH DE number 1057403