represents a survival distribution with event times ei.

represents a survival distribution where events ei occur with censor weights cwi.

Details and OptionsDetails and Options

  • SurvivalDistribution is used in survival, reliability, and duration analysis.
  • SurvivalDistribution produces a DataDistribution object representing the EmpiricalDistribution of censored lifetime data.
  • The following individual event specifications can be used for ei:
  • tino censoring; event happens at tti
    {ti,}right censoring; event happens at some t where tit
    {-,ti}left censoring; event happens at some t where t<ti
    {ti,min,ti,max}interval censoring; event happens at some t where ti,min<tti,max
  • The following individual censor weight specifications can be used for cwi:
  • cici events at ei
    {ci,ri}ci events and ri right-censored events at ei
    {ci,ri,li}ci events, ri right-censored, and li left-censored events at ei
  • In SurvivalDistribution, the lists of event times and weights must be the same length.
  • EventData[{t1,},{i1,}] can be used to transform event times {t1,} with censoring vector {i1,} to the form {{t1,min,t1,max},}.
  • The following options can be given:
  • MethodAutomaticmethod to use
    WorkingPrecisionAutomaticprecision to use in internal computations
  • SurvivalDistribution automatically chooses the method most appropriate to the data. The KaplanMeier estimator is used for right-censored data. For other types of censoring, the estimate is constructed using a self-consistency approach. Different methods may only support some types of censoring.
  • Possible settings for Method include:
  • Automaticautomatically select the most appropriate method
    "Turnbull"Turnbull algorithm for interval-censored data
    "KaplanMeier"product limit estimator for right-censored data
    "NelsonAalen"based on the NelsonAalen cumulative hazard estimator
    "Noncensored"censoring is ignored and interval midpoints are used
    "SelfConsistency"Turnbull algorithm for doubly censored data
  • SurvivalDistribution can be used with such functions as Mean, CDF, and RandomVariate.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Create a survival distribution from some right-censored survival data:

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Visualize the survival function:

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Compute moments and quantiles:

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Introduced in 2010