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# Accession Number:

## AD0270015

# Title:

## PROPERTIES OF PROBABILITY DISTRIBUTIONS WITH MONOTONE HAZARD RATE

# Descriptive Note:

# Corporate Author:

## BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH

# Report Date:

## 1962-01-01

# Pagination or Media Count:

##
1.0

# Abstract:

## Properties of distribution functions F or their densities f are related to properties of the corres onding hazard rate q defined by qx equals fx 1 - Fx . Interest in the hazard rate is derived from its probabilistic interpretation if, for example, F is a life distribution, qxdx is the conditional probability of death in x, x dx given survival to age x. Because of this interpretation f is assumed to be the density of a positive random variable, although for many of the results this is not necessary. The hazard rate is important in a number of applications, and is known by a variety of names. It is used by actuaries under the name of force of mortality to compute mortality tables, and its reciprocal is known to statisticians as Mills ratio. In the analysis of extreme value distributions it is called the intensity function, and in reliability theory it is usually referred to as the failure rate. A number of general results are obtained, but particular attention is paid to densities with monotone hazard rate. Autho

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#