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 .

HazardFunction[dist]
gives the hazard function as a pure function.

DetailsDetails

  • 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 , 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].

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

A hazard function for a continuous univariate distribution:

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The hazard function for a discrete univariate distribution:

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A hazard function for a continuous multivariate distribution:

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A hazard function for a discrete multivariate distribution:

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Introduced in 2010
(8.0)