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[x<x+dxConditionedx, Distributeddist] for infinitesimal dx. »
  • For discrete distributions, HazardFunction[dist, x] is equivalent to Probability[=xConditionedx, Distributeddist].
  • For continuous multivariate distributions, HazardFunction[dist, {x1, ..., xn}]dx1 dxn is equivalent to Probability[x11<x1+dx1xnn<xn+dxnConditioned1≥x1n≥xn, {1, ..., n}Distributeddist].
  • For discrete multivariate distributions, HazardFunction[dist, {x1, ..., xn}] is equivalent to Probability[1=x1 n=xnConditioned1x1nxn, {1, ..., n}Distributeddist].

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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