This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# HazardFunction

 HazardFunction gives the hazard function for the symbolic distribution dist evaluated at x. HazardFunctiongives the multivariate hazard function for the symbolic distribution dist evaluated at . HazardFunction[dist]gives the hazard function as a pure function.
• For continuous distributions, HazardFunction[dist, x] dx gives the probability that an observed value lies between x and , given that it is larger than x for infinitesimal dx.
A hazard function for a continuous univariate distribution:
The hazard function for a discrete univariate distribution:
A hazard function for a continuous multivariate distribution:
A hazard function for a discrete multivariate distribution:
A hazard function for a continuous univariate distribution:
 Out[1]=
 Out[2]=

The hazard function for a discrete univariate distribution:
 Out[1]=
 Out[2]=

A hazard function for a continuous multivariate distribution:
 Out[1]=

A hazard function for a discrete multivariate distribution:
 Out[1]=
 Scope   (16)
Obtain exact numeric results:
Obtain a machine-precision result:
Obtain a result at any precision for a continuous distribution:
Obtain a result at any precision for a discrete distribution with inexact parameters:
Hazard function for a multivariate distribution:
Obtain a symbolic expression for the hazard function:
Hazard function for nonparametric distributions:
Compare with the value for the underlying parametric distribution:
Plot the survival function for a histogram distribution:
Plot of the survival function of a bivariate smooth kernel distribution:
Product of independent distributions:
Component mixture distribution:
Quadratic transformation of a discrete distribution:
Truncated distribution:
A copula distribution:
Formula distributions defined by its PDF:
Defined by its CDF:
Defined by its survival function:
Marginal distribution:
 Applications   (3)
Find the mortality rate for lifetime distributions including exponential distribution:
Gompertz distribution:
Study the hazard function for a family of Weibull distributions:
With , used is better than new:
With , used is as good as new:
With , used is worse than new:
A casino offers you a game where you pay amount to participate and then choose a stake amount . A positive continuous random variable following a known distribution is then generated. If you collect the stake; otherwise you lose. Find the value that maximizes the profit:
Find the equation for the maximum of the expected gain:
Assuming WeibullDistribution, find the optimal stake size:
Compute the hazard function using the definition as conditional probability:
The hazard function is a ratio of the PDF and the survival function :
Symbolic closed forms do not exist for some distributions:
Numerical evaluation works:
Substitution of invalid values into symbolic outputs gives results that are not meaningful:
Passing it as an argument, it stays unevaluated:
New in 8