The multivariate hazard gradient and moments of the truncated multinormal distribution

Abstract

It is well known that the expectation and variance of a truncated normal distribution can be simply expressed in terms of the hazard rate function. This paper shows that it is possible to express the expectation and covariance matrices of a truncated multinormal distribution with similarly simple expressions in which the hazard rate function is generalized to thevector multivariate hazard rate(also: hazard gradient) of Johnson and Kotz. This provides a concise computational form for the mutivariate moments and lends support to the contention that the hazard gradient is the appropriate generalization of the univariate hazard rate.

Keywords:

• TRUNCATED NORMAL
• HAZARD RATE
• CENSORED REGRESSION
• LIFETIME
• RELIABILITY