hazard function

Let Y be a random variableMathworldPlanetmath with probability density functionMathworldPlanetmath fY(y). Then the hazard functionMathworldPlanetmath h(y) is defined to be:


where S(y) is the survivor function and Y is the survival time.

The hazard function is the rate of probability of death (non survival) is changing at time Y=y, given survival up to time y:


The cumulative hazard function, H(y) of Y is defined as


From this definition, we see that H(y)=-lnS(y).

Examples. The hazard functions for the three most widely used probability density functions for survival time are:

Title hazard function
Canonical name HazardFunction
Date of creation 2013-03-22 14:27:45
Last modified on 2013-03-22 14:27:45
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 6
Author CWoo (3771)
Entry type Definition
Classification msc 62N99
Classification msc 62P05
Defines cumulative hazard function