# HazardFunction

HazardFunction[dist,x]

gives the hazard function for the symbolic distribution dist evaluated at x.

HazardFunction[dist,{x1,x2,}]

gives the multivariate hazard function for the symbolic distribution dist evaluated at {x1,x2,}.

HazardFunction[dist]

gives the hazard function as a pure function.

# Details

• HazardFunction is also known as a force of mortality.
• For continuous distributions, HazardFunction[dist,x] dx gives the probability that an observed value lies between x and x+dx, given that it is larger than x for infinitesimal dx.
• For continuous distributions, HazardFunction[dist,x] dx is equivalent to Probability[xξ<x+dxξx,ξdist] for infinitesimal dx. »
• For discrete distributions, HazardFunction[dist,x] is equivalent to Probability[ξxξx,ξdist].
• For continuous multivariate distributions, HazardFunction[dist,{x1,,xn}]dx1 dxn is equivalent to Probability[x1ξ1<x1+dx1xnξn<xn+dxnξ1x1ξnxn,{ξ1,,ξn}dist].
• For discrete multivariate distributions, HazardFunction[dist,{x1,,xn}] is equivalent to Probability[ξ1x1 ξnxnξ1x1ξnxn,{ξ1,,ξn}dist].

# Examples

open allclose all

## Basic Examples(4)

A hazard function for a continuous univariate distribution:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=

The hazard function for a discrete univariate distribution:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]=

A hazard function for a continuous multivariate distribution:

 In[1]:=
 Out[1]=

A hazard function for a discrete multivariate distribution:

 In[1]:=
 Out[1]=