public void EmpiricalHazardConstructorTest3()
{
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 };
EmpiricalHazardDistribution distribution = new EmpiricalHazardDistribution(times, values);
double mean = distribution.Mean; // 0.93696461879063664
double median = distribution.Median; // 3.9999999151458066
double var = distribution.Variance; // 2.0441627748096289
double chf = distribution.CumulativeHazardFunction(x: 4.2); // 1.55
double cdf = distribution.DistributionFunction(x: 4.2); // 0.7877520261732569
double pdf = distribution.ProbabilityDensityFunction(x: 4.2); // 0.046694554241883471
double lpdf = distribution.LogProbabilityDensityFunction(x: 4.2); // -3.0641277326297756
double hf = distribution.HazardFunction(x: 4.2); // 0.22
double ccdf = distribution.ComplementaryDistributionFunction(x: 4.2); // 0.21224797382674304
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.3483975243778978
string str = distribution.ToString(); // H(x; v, t)
Assert.AreEqual(0.93696461879063664, mean);
Assert.AreEqual(3.9999999151458066, median, 1e-6);
Assert.AreEqual(2.0441627748096289, var);
Assert.AreEqual(1.55, chf);
Assert.AreEqual(0.7877520261732569, cdf);
Assert.AreEqual(0.046694554241883471, pdf);
Assert.AreEqual(-3.0641277326297756, lpdf);
Assert.AreEqual(0.22, hf);
Assert.AreEqual(0.21224797382674304, ccdf);
Assert.AreEqual(4.3483975243778978, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
}
public void EmpiricalHazardConstructorTest3()
{
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 };
EmpiricalHazardDistribution distribution = new EmpiricalHazardDistribution(times, values);
double mean = distribution.Mean; // 0.93696461879063664
double median = distribution.Median; // 3.9999999151458066
double var = distribution.Variance; // 2.0441627748096289
double chf = distribution.CumulativeHazardFunction(x: 4.2); // 1.55
double cdf = distribution.DistributionFunction(x: 4.2); // 0.7877520261732569
double pdf = distribution.ProbabilityDensityFunction(x: 4.2); // 0.046694554241883471
double lpdf = distribution.LogProbabilityDensityFunction(x: 4.2); // -3.0641277326297756
double hf = distribution.HazardFunction(x: 4.2); // 0.22
double ccdf = distribution.ComplementaryDistributionFunction(x: 4.2); // 0.21224797382674304
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.3483975243778978
string str = distribution.ToString(); // H(x; v, t)
Assert.AreEqual(0.93696461879063664, mean);
Assert.AreEqual(3.9999999151458066, median, 1e-6);
Assert.AreEqual(2.0441627748096289, var);
Assert.AreEqual(1.55, chf);
Assert.AreEqual(0.7877520261732569, cdf);
Assert.AreEqual(0.046694554241883471, pdf);
Assert.AreEqual(-3.0641277326297756, lpdf);
Assert.AreEqual(0.22, hf);
Assert.AreEqual(0.21224797382674304, ccdf);
Assert.AreEqual(4.3483975243778978, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
}
public void inverse_cdf()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125,0,
0.166666666666667, 0.2, 0, 0.5, 0
};
var distribution = new EmpiricalHazardDistribution(times, hazards);
Assert.AreEqual(0, distribution.Support.Min);
Assert.AreEqual(22, distribution.Support.Max);
Assert.AreEqual(0, distribution.InverseDistributionFunction(0));
Assert.AreEqual(22, distribution.InverseDistributionFunction(1));
Assert.AreEqual(22, distribution.InverseDistributionFunction(0.999));
Assert.AreEqual(0, distribution.DistributionFunction(0));
Assert.AreEqual(0.1051606831856301d, distribution.DistributionFunction(1));
Assert.AreEqual(0.1593762566654946d, distribution.DistributionFunction(2));
Assert.AreEqual(0.78033456236530996d, distribution.DistributionFunction(20));
Assert.AreEqual(0.78033456236530996d, distribution.DistributionFunction(21));
Assert.AreEqual(0.78033456236530996d, distribution.InnerDistributionFunction(21));
Assert.AreEqual(1.0, distribution.DistributionFunction(22));
Assert.AreEqual(1.0, distribution.InnerDistributionFunction(22));
Assert.AreEqual(1.0, distribution.InnerDistributionFunction(23));
Assert.AreEqual(1.0, distribution.InnerDistributionFunction(24));
Assert.AreEqual(1.0, distribution.DistributionFunction(22));
double[] percentiles = Vector.Interval(0.0, 1.0, stepSize: 0.1);
for (int i = 0; i < percentiles.Length; i++)
{
double p = percentiles[i];
double icdf = distribution.InverseDistributionFunction(p);
double cdf = distribution.DistributionFunction(icdf);
Assert.AreEqual(cdf, p, 0.1);
}
}
public void MedianTest()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
EmpiricalHazardDistribution target =
new EmpiricalHazardDistribution(times, values);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void MedianTest_KaplanMeier()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
var target = new EmpiricalHazardDistribution(times, values, SurvivalEstimator.KaplanMeier);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
Assert.AreEqual(1, target.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, target.ComplementaryDistributionFunction(Double.PositiveInfinity));
}
public void DocumentationExample_Aalen()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125,0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards);
// Common measures
double mean = distribution.Mean; // 6.1658527179584119
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 44.101147497430993
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.724725178982381
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.FlemingHarrington, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(6.1658527179584119, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(44.101147497430993, var);
Assert.AreEqual(0.32196275946275932, chf);
Assert.AreEqual(0.275274821017619, cdf);
Assert.AreEqual(0.055748090690952365, pdf);
Assert.AreEqual(-2.8869121169242962, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.724725178982381, ccdf);
Assert.AreEqual(4.4588994137113307, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
{
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}
}
public void DocumentationExample_KaplanMeier()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125,0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards, SurvivalEstimator.KaplanMeier);
// Common measures
double mean = distribution.Mean; // 5.49198237428757
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 39.83481657555663
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.018754904264376961
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.KaplanMeier, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(5.49198237428757, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(39.83481657555663, var);
Assert.AreEqual(0.33647223662121273, chf);
Assert.AreEqual(0.28571428571428559, cdf);
Assert.AreEqual(0.054945054945054937, pdf);
Assert.AreEqual(-2.9014215940827497, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.71428571428571441, ccdf);
Assert.AreEqual(5.8785425101214548, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
{
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}
}
public void MedianTest()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
EmpiricalHazardDistribution target =
new EmpiricalHazardDistribution(times, values);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void MedianTest_KaplanMeier()
{
double[] values =
{
0.0000000000000000, 0.0351683340828711, 0.0267358118285064,
0.0000000000000000, 0.0103643094219679, 0.0000000000000000,
0.0000000000000000, 0.0000000000000000, 0.0000000000000000,
0.000762266794052363, 0.000000000000000
};
double[] times =
{
11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1
};
var target = new EmpiricalHazardDistribution(times, values, SurvivalEstimator.KaplanMeier);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
Assert.AreEqual(1, target.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, target.ComplementaryDistributionFunction(Double.PositiveInfinity));
}
public void DocumentationExample_Aalen()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125, 0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards);
// Common measures
double mean = distribution.Mean; // 6.1658527179584119
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 44.101147497430993
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.724725178982381
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.FlemingHarrington, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(6.1658527179584119, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(44.101147497430993, var);
Assert.AreEqual(0.32196275946275932, chf);
Assert.AreEqual(0.275274821017619, cdf);
Assert.AreEqual(0.055748090690952365, pdf);
Assert.AreEqual(-2.8869121169242962, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.724725178982381, ccdf);
Assert.AreEqual(4.4588994137113307, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}
public void DocumentationExample_KaplanMeier()
{
// Consider the following hazard rates, occurring at the given time steps
double[] times = { 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 21 };
double[] hazards =
{
0, 0.111111111111111, 0.0625, 0.0714285714285714, 0.0769230769230769,
0, 0.0909090909090909, 0, 0.111111111111111, 0.125, 0,
0.166666666666667, 0.2, 0, 0.5, 0
};
// Create a new distribution given the observations and event times
var distribution = new EmpiricalHazardDistribution(times, hazards, SurvivalEstimator.KaplanMeier);
// Common measures
double mean = distribution.Mean; // 5.49198237428757
double median = distribution.Median; // 11.999999704601453
double var = distribution.Variance; // 39.83481657555663
// Cumulative distribution functions
double cdf = distribution.DistributionFunction(x: 4); // 0.275274821017619
double ccdf = distribution.ComplementaryDistributionFunction(x: 4); // 0.018754904264376961
double icdf = distribution.InverseDistributionFunction(p: cdf); // 4.4588994137113307
// Probability density functions
double pdf = distribution.ProbabilityDensityFunction(x: 4); // 0.055748090690952365
double lpdf = distribution.LogProbabilityDensityFunction(x: 4); // -2.8869121169242962
// Hazard (failure rate) functions
double hf = distribution.HazardFunction(x: 4); // 0.0769230769230769
double chf = distribution.CumulativeHazardFunction(x: 4); // 0.32196275946275932
string str = distribution.ToString(); // H(x; v, t)
try { double mode = distribution.Mode; Assert.Fail(); }
catch { }
Assert.AreEqual(SurvivalEstimator.KaplanMeier, distribution.Estimator);
Assert.AreEqual(1, distribution.ComplementaryDistributionFunction(0));
Assert.AreEqual(0, distribution.ComplementaryDistributionFunction(Double.PositiveInfinity));
Assert.AreEqual(5.49198237428757, mean);
Assert.AreEqual(11.999999704601453, median, 1e-6);
Assert.AreEqual(39.83481657555663, var);
Assert.AreEqual(0.33647223662121273, chf);
Assert.AreEqual(0.28571428571428559, cdf);
Assert.AreEqual(0.054945054945054937, pdf);
Assert.AreEqual(-2.9014215940827497, lpdf);
Assert.AreEqual(0.0769230769230769, hf);
Assert.AreEqual(0.71428571428571441, ccdf);
Assert.AreEqual(5.8785425101214548, icdf, 1e-8);
Assert.AreEqual("H(x; v, t)", str);
var range1 = distribution.GetRange(0.95);
var range2 = distribution.GetRange(0.99);
var range3 = distribution.GetRange(0.01);
Assert.AreEqual(1, range1.Min, 1e-3);
Assert.AreEqual(20.562, range1.Max, 1e-3);
Assert.AreEqual(1, range2.Min, 1e-3);
Assert.AreEqual(20.562, range2.Max, 1e-3);
Assert.AreEqual(1, range3.Min, 1e-3);
Assert.AreEqual(20.562, range3.Max, 1e-3);
for (int i = 0; i < hazards.Length; i++)
Assert.AreEqual(hazards[i], distribution.HazardFunction(times[i]));
}