HazardFunction

HazardFunction[dist,x]

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

HazardFunction[dist,{x1,x2,…}]

gives the multivariate hazard function for the 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[x≤ξ<x+dxξ≥x,ξdist] for infinitesimal dx. »
  • For discrete distributions, HazardFunction[dist,x] is equivalent to Probability[ξxξ≥x,ξdist].
  • For continuous multivariate distributions, HazardFunction[dist,{x1,…,xn}]dx1 ⋯ dxn is equivalent to Probability[x1≤ξ1<x1+dx1∧⋯∧xn≤ξn<xn+dxnξ1≥x1∧⋯∧ξn≥xn,{ξ1,…,ξn}dist].
  • For discrete multivariate distributions, HazardFunction[dist,{x1,…,xn}] is equivalent to Probability[ξ1x1∧⋯ ∧ξnxnξ1≥x1∧⋯∧ξn≥xn,{ξ1,…,ξn}dist].

Examples

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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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Scope  (20)

Generalizations & Extensions  (1)

Applications  (4)

Properties & Relations  (3)

Possible Issues  (2)

Introduced in 2010
(8.0)