EmpiricalHazardDistribution Class 
Namespace: Accord.Statistics.Distributions.Univariate
[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>
The EmpiricalHazardDistribution type exposes the following members.
Name  Description  

EmpiricalHazardDistribution 
Initializes a new instance of the EmpiricalHazardDistribution class.
 
EmpiricalHazardDistribution(SurvivalEstimator) 
Initializes a new instance of the EmpiricalHazardDistribution class.
 
EmpiricalHazardDistribution(Double, Double) 
Initializes a new instance of the EmpiricalHazardDistribution class.
 
EmpiricalHazardDistribution(Double, Double, SurvivalEstimator) 
Initializes a new instance of the EmpiricalHazardDistribution class.

Name  Description  

Entropy 
This method is not supported.
(Overrides UnivariateContinuousDistributionEntropy.)  
Estimator 
Gets the survival function estimator being used in this distribution.
 
Hazards 
Gets the hazard rate values at each time step.
 
Mean 
Gets the mean for this distribution.
(Overrides UnivariateContinuousDistributionMean.)  
Median 
Gets the median for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
Mode 
This method is not supported.
(Overrides UnivariateContinuousDistributionMode.)  
Quartiles 
Gets the Quartiles for this distribution.
(Inherited from UnivariateContinuousDistribution.)  
StandardDeviation 
Gets the Standard Deviation (the square root of
the variance) for the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Support 
Gets the support interval for this distribution.
(Overrides UnivariateContinuousDistributionSupport.)  
Survivals 
Gets the survival values at each time step.
 
Times 
Gets the time steps of the hazard density values.
 
Variance 
Gets the variance for this distribution.
(Overrides UnivariateContinuousDistributionVariance.) 
Name  Description  

Clone 
Creates a new object that is a copy of the current instance.
(Overrides DistributionBaseClone.)  
ComplementaryDistributionFunction 
Gets the complementary cumulative distribution function
(ccdf) for this distribution evaluated at point x.
This function is also known as the Survival function.
(Overrides UnivariateContinuousDistributionComplementaryDistributionFunction(Double).)  
CumulativeHazardFunction 
Gets the cumulative hazard function for this
distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionCumulativeHazardFunction(Double).)  
DistributionFunction(Double) 
Gets the cumulative distribution function (cdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionDistributionFunction(Double).)  
DistributionFunction(Double, Double) 
Gets the cumulative distribution function (cdf) for this
distribution in the semiclosed interval (a; b] given as
P(a < X ≤ b).
(Inherited from UnivariateContinuousDistribution.)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
Estimate(Double, SurvivalOutcome) 
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.
 
Estimate(Double, SurvivalOutcome, 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.
 
Estimate(Double, SurvivalOutcome, Double) 
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.
 
Estimate(Double, Int32, 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.
 
Estimate(Double, Int32, Double) 
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.
 
Estimate(Double, SurvivalOutcome, SurvivalEstimator, HazardEstimator) 
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.
 
Estimate(Double, Int32, SurvivalEstimator, HazardEstimator) 
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.
 
Estimate(Double, SurvivalOutcome, 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.
 
Estimate(Double, SurvivalOutcome, Double, SurvivalEstimator, HazardEstimator) 
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.
 
Estimate(Double, Int32, 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.
 
Estimate(Double, Int32, Double, SurvivalEstimator, HazardEstimator) 
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.
 
Estimate(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.
 
Estimate(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.
 
Finalize  Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)  
Fit(Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Double) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Int32) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Fit(Double, Double, EmpiricalHazardOptions) 
Fits the underlying distribution to a given set of observations.
 
Fit(Double, Double, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Overrides UnivariateContinuousDistributionFit(Double, Double, IFittingOptions).)  
Fit(Double, Double, SurvivalOptions) 
Fits the underlying distribution to a given set of observations.
 
Fit(Double, Int32, IFittingOptions) 
Fits the underlying distribution to a given set of observations.
(Inherited from UnivariateContinuousDistribution.)  
Generate 
Generates a random observation from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
Generate(Int32, Double) 
Generates a random vector of observations from the current distribution.
(Inherited from UnivariateContinuousDistribution.)  
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetRange 
Gets the distribution range within a given percentile.
(Inherited from UnivariateContinuousDistribution.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
HazardFunction 
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).)  
InverseDistributionFunction 
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.)  
LogCumulativeHazardFunction 
Gets the log of the cumulative hazard function for this
distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
LogProbabilityDensityFunction 
Gets the logprobability density function (pdf) for
this distribution evaluated at point x.
(Inherited from UnivariateContinuousDistribution.)  
MemberwiseClone  Creates a shallow copy of the current Object. (Inherited from Object.)  
ProbabilityDensityFunction 
Gets the probability density function (pdf) for
this distribution evaluated at point x.
(Overrides UnivariateContinuousDistributionProbabilityDensityFunction(Double).)  
QuantileDensityFunction 
Gets the first derivative of the
inverse distribution function (icdf) for this distribution evaluated
at probability p.
(Inherited from UnivariateContinuousDistribution.)  
Sort(Double, SurvivalOutcome) 
Sorts timecensored 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.
 
Sort(Double, SurvivalOutcome, Double) 
Sorts timecensored 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.
 
Sort(Double, SurvivalOutcome, Double) 
Sorts timecensored 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.
 
ToString 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(IFormatProvider) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String) 
Returns a String that represents this instance.
(Inherited from DistributionBase.)  
ToString(String, IFormatProvider) 
Returns a String that represents this instance.
(Overrides DistributionBaseToString(String, IFormatProvider).) 
Name  Description  

HasMethod 
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)  
ToT  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.)  
ToT  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 Matrix.) 
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.htmThe following example shows how to construct an empirical hazards function from a set of hazard values at the given time instants.
// 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)