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EmpiricalHazardDistribution Class
Empirical Hazard Distribution.
Inheritance Hierarchy
SystemObject
  Accord.Statistics.DistributionsDistributionBase
    Accord.Statistics.Distributions.UnivariateUnivariateContinuousDistribution
      Accord.Statistics.Distributions.UnivariateEmpiricalHazardDistribution

Namespace:  Accord.Statistics.Distributions.Univariate
Assembly:  Accord.Statistics (in Accord.Statistics.dll) Version: 3.8.0
Syntax
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[SerializableAttribute]
public class EmpiricalHazardDistribution : UnivariateContinuousDistribution, 
	IFittableDistribution<double, SurvivalOptions>, IFittable<double, SurvivalOptions>, 
	IFittable<double>, IFittableDistribution<double>, IDistribution<double>, 
	IDistribution, ICloneable, IFittableDistribution<double, EmpiricalHazardOptions>, 
	IFittable<double, EmpiricalHazardOptions>
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The EmpiricalHazardDistribution type exposes the following members.

Constructors
Properties
  NameDescription
Public propertyEntropy
This method is not supported.
(Overrides UnivariateContinuousDistributionEntropy.)
Public propertyEstimator
Gets the survival function estimator being used in this distribution.
Public propertyHazards
Gets the hazard rate values at each time step.
Public propertyMean
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.)
Public propertyMedian
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyMode
This method is not supported.
(Overrides UnivariateContinuousDistributionMode.)
Public propertyQuartiles
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertyStandardDeviation
Gets the Standard Deviation (the square root of the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public propertySupport
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.)
Public propertySurvivals
Gets the survival values at each time step.
Public propertyTimes
Gets the time steps of the hazard density values.
Public propertyVariance
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.)
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)
Public methodComplementaryDistributionFunction
Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.
(Inherited from UnivariateContinuousDistribution.)
Public methodCumulativeHazardFunction
Gets the cumulative hazard function for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionCumulativeHazardFunction(Double).)
Public methodDistributionFunction(Double)
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodDistributionFunction(Double, Double)
Gets the cumulative distribution function (cdf) for this distribution in the semi-closed interval (a; b] given as P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Public methodStatic memberEstimate(Double, Double, SurvivalEstimator, HazardEstimator, HazardTiesMethod)
Estimates an Empirical Hazards distribution considering event times and the outcome of the observed sample at the time of event, plus additional parameters for the hazard estimation.
Public methodStatic memberEstimate(Double, SurvivalOutcome, Double, SurvivalEstimator, HazardEstimator, HazardTiesMethod)
Estimates an Empirical Hazards distribution considering event times and the outcome of the observed sample at the time of event, plus additional parameters for the hazard estimation.
Public methodStatic memberEstimate(Double, Int32, Double, SurvivalEstimator, HazardEstimator, HazardTiesMethod)
Estimates an Empirical Hazards distribution considering event times and the outcome of the observed sample at the time of event, plus additional parameters for the hazard estimation.
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodCode exampleFit(Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Double)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodCode exampleFit(Double, Int32)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodFit(Double, Double, EmpiricalHazardOptions)
Fits the underlying distribution to a given set of observations.
Public methodFit(Double, Double, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)
Public methodFit(Double, Double, SurvivalOptions)
Fits the underlying distribution to a given set of observations.
Public methodCode exampleFit(Double, Int32, IFittingOptions)
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Random)
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGenerate(Int32, Double, Random)
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRange
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazardFunction
Gets the hazard function, also known as the failure rate or the conditional failure density function for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionHazardFunction(Double).)
Protected methodInnerComplementaryDistributionFunction
Gets the complementary cumulative distribution function (ccdf) for this distribution evaluated at point x. This function is also known as the Survival function.
(Overrides UnivariateContinuousDistributionInnerComplementaryDistributionFunction(Double).)
Protected methodInnerDistributionFunction
Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerDistributionFunction(Double).)
Protected methodInnerInverseDistributionFunction
Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodInnerProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionInnerProbabilityDensityFunction(Double).)
Public methodInverseDistributionFunction
Gets the inverse of the cumulative distribution function (icdf) for this distribution evaluated at probability p. This function is also known as the Quantile function.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogCumulativeHazardFunction
Gets the log of the cumulative hazard function for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodLogProbabilityDensityFunction
Gets the log-probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbabilityDensityFunction
Gets the probability density function (pdf) for this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)
Public methodQuantileDensityFunction
Gets the first derivative of the inverse distribution function (icdf) for this distribution evaluated at probability p.
(Inherited from UnivariateContinuousDistribution.)
Public methodStatic memberSort(Double, SurvivalOutcome)
Sorts time-censored events considering their time of occurrence and the type of event. Events are first sorted in decreased order of occurrence, and then with failures coming before censoring.
Public methodStatic memberSort(Double, SurvivalOutcome, Double)
Sorts time-censored events considering their time of occurrence and the type of event. Events are first sorted in decreased order of occurrence, and then with failures coming before censoring.
Public methodStatic memberSort(Double, SurvivalOutcome, Double)
Sorts time-censored events considering their time of occurrence and the type of event. Events are first sorted in decreased order of occurrence, and then with failures coming before censoring.
Public methodToString
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(IFormatProvider)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String)
Returns a String that represents this instance.
(Inherited from DistributionBase.)
Public methodToString(String, IFormatProvider)
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodTo(Type)Overloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
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Remarks

The Empirical Hazard (or Survival) Distribution can be used as an estimative of the true Survival function for a dataset which does not relies on distribution or model assumptions about the data.

The most direct use for this class is in Survival Analysis, such as when using or creating Cox's Proportional Hazards models.

// references http://www.statsdirect.com/help/default.htm#survival_analysis/kaplan_meier.htm
Examples

The following example shows how to construct an empirical hazards function from a set of hazard values at the given time instants.

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// Consider the following observations, occurring at the given time steps
double[] times = { 11, 10, 9, 8, 6, 5, 4, 2 };
double[] values = { 0.22, 0.67, 1.00, 0.18, 1.00, 1.00, 1.00, 0.55 };

// Create a new empirical distribution function given the observations and event times
EmpiricalHazardDistribution distribution = new EmpiricalHazardDistribution(times, values);

// Common measures
double mean   = distribution.Mean;     // 2.1994135014183138
double median = distribution.Median;   // 3.9999999151458066
double var    = distribution.Variance; // 4.2044065839577112

// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4.2);               // 0.7877520261732569
double ccdf = distribution.ComplementaryDistributionFunction(x: 4.2); // 0.21224797382674304
double icdf = distribution.InverseDistributionFunction(p: cdf);       // 4.3304819115496436

// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4.2);     // 0.21224797382674304
double lpdf = distribution.LogProbabilityDensityFunction(x: 4.2); // -1.55

// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4.2);            // 1.0
double chf = distribution.CumulativeHazardFunction(x: 4.2); // 1.55

// String representation
string str = distribution.ToString(); // H(x; v, t)
See Also