public void BetaMeanTest()
{
double alpha = 0.42;
double beta = 1.57;
BetaDistribution betaDistribution = new BetaDistribution(alpha, beta);
double mean = betaDistribution.Mean; // 0.21105527638190955
double median = betaDistribution.Median; // 0.11577706212908731
double var = betaDistribution.Variance; // 0.055689279830523512
double mode = betaDistribution.Mode; // 57.999999999999957
double chf = betaDistribution.CumulativeHazardFunction(x: 0.27); // 1.1828193992944409
double cdf = betaDistribution.DistributionFunction(x: 0.27); // 0.69358638272337991
double pdf = betaDistribution.ProbabilityDensityFunction(x: 0.27); // 0.94644031936694828
double lpdf = betaDistribution.LogProbabilityDensityFunction(x: 0.27); // -0.055047364344046057
double hf = betaDistribution.HazardFunction(x: 0.27); // 3.0887671630877072
double ccdf = betaDistribution.ComplementaryDistributionFunction(x: 0.27); // 0.30641361727662009
double icdf = betaDistribution.InverseDistributionFunction(p: cdf); // 0.26999999068687469
string str = betaDistribution.ToString(System.Globalization.CultureInfo.InvariantCulture); // "B(x; α = 0.42, β = 1.57)
Assert.AreEqual(0.21105527638190955, mean);
Assert.AreEqual(0.11577706212908731, median);
Assert.AreEqual(57.999999999999957, mode);
Assert.AreEqual(0.055689279830523512, var);
Assert.AreEqual(1.1828193992944409, chf);
Assert.AreEqual(0.69358638272337991, cdf);
Assert.AreEqual(0.94644031936694828, pdf);
Assert.AreEqual(-0.055047364344046057, lpdf);
Assert.AreEqual(3.0887671630877072, hf);
Assert.AreEqual(0.30641361727662009, ccdf);
Assert.AreEqual(0.27, icdf, 1e-10);
Assert.AreEqual("B(x; α = 0.42, β = 1.57)", str);
Assert.IsFalse(Double.IsNaN(median));
var range1 = betaDistribution.GetRange(0.95);
var range2 = betaDistribution.GetRange(0.99);
var range3 = betaDistribution.GetRange(0.01);
Assert.AreEqual(0.00045925525776717733, range1.Min);
Assert.AreEqual(0.72381020663218609, range1.Max);
Assert.AreEqual(0.0000099485893745082635, range2.Min);
Assert.AreEqual(0.89625688707910811, range2.Max);
Assert.AreEqual(0.0000099485893745082432, range3.Min);
Assert.AreEqual(0.89625688707910811, range3.Max);
Assert.AreEqual(0, betaDistribution.Support.Min);
Assert.AreEqual(1, betaDistribution.Support.Max);
Assert.AreEqual(betaDistribution.InverseDistributionFunction(0), betaDistribution.Support.Min);
Assert.AreEqual(betaDistribution.InverseDistributionFunction(1), betaDistribution.Support.Max);
}
public static (double faintSuspicion, double strongSuspicion) GetSuspicionLevels(double mean, double sigma, double faintSuspicionCoefficient, double strongSuspicionCoefficient)
{
if (Math.Abs(sigma) < 1e-7)
{
return(1, 1);
}
var(alpha, beta) = GetBetaParameters(mean, sigma);
var betaDistribution = new BetaDistribution(alpha, beta);
var faintSigmaToProbability = new NormalDistribution(0, 1).DistributionFunction(faintSuspicionCoefficient);
var strongSigmaToProbability = new NormalDistribution(0, 1).DistributionFunction(strongSuspicionCoefficient);
var faintSuspicion = betaDistribution.InverseDistributionFunction(faintSigmaToProbability);
var strongSuspicion = betaDistribution.InverseDistributionFunction(strongSigmaToProbability);
return(faintSuspicion, strongSuspicion);
}
public void BetaMeanTest()
{
double alpha = 0.42;
double beta = 1.57;
BetaDistribution betaDistribution = new BetaDistribution(alpha, beta);
double mean = betaDistribution.Mean; // 0.21105527638190955
double median = betaDistribution.Median; // 0.11577706212908731
double var = betaDistribution.Variance; // 0.055689279830523512
double chf = betaDistribution.CumulativeHazardFunction(x: 0.27); // 1.1828193992944409
double cdf = betaDistribution.DistributionFunction(x: 0.27); // 0.69358638272337991
double pdf = betaDistribution.ProbabilityDensityFunction(x: 0.27); // 0.94644031936694828
double lpdf = betaDistribution.LogProbabilityDensityFunction(x: 0.27); // -0.055047364344046057
double hf = betaDistribution.HazardFunction(x: 0.27); // 3.0887671630877072
double ccdf = betaDistribution.ComplementaryDistributionFunction(x: 0.27); // 0.30641361727662009
double icdf = betaDistribution.InverseDistributionFunction(p: cdf); // 0.26999999068687469
string str = betaDistribution.ToString(System.Globalization.CultureInfo.InvariantCulture); // "B(x; α = 0.42, β = 1.57)
Assert.AreEqual(0.21105527638190955, mean);
Assert.AreEqual(0.11577706212908731, median);
Assert.AreEqual(0.055689279830523512, var);
Assert.AreEqual(1.1828193992944409, chf);
Assert.AreEqual(0.69358638272337991, cdf);
Assert.AreEqual(0.94644031936694828, pdf);
Assert.AreEqual(-0.055047364344046057, lpdf);
Assert.AreEqual(3.0887671630877072, hf);
Assert.AreEqual(0.30641361727662009, ccdf);
Assert.AreEqual(0.27, icdf, 1e-10);
Assert.AreEqual("B(x; α = 0.42, β = 1.57)", str);
Assert.IsFalse(Double.IsNaN(median));
}
public void MedianTest()
{
double alpha = 0.42;
double beta = 1.57;
BetaDistribution target = new BetaDistribution(alpha, beta);
Assert.AreEqual(target.Median, target.InverseDistributionFunction(0.5));
}
public void BetaMeanTest2()
{
int trials = 161750;
int successes = 10007;
BetaDistribution betaDistribution = new BetaDistribution(successes, trials);
double mean = betaDistribution.Mean; // 0.06187249616697166
double median = betaDistribution.Median; // 0.06187069085946604
double p025 = betaDistribution.InverseDistributionFunction(p: 0.025); // 0.06070354581334864
double p975 = betaDistribution.InverseDistributionFunction(p: 0.975); // 0.0630517079399996
string str = betaDistribution.ToString();
Assert.AreEqual(0.06187249616697166, mean);
Assert.AreEqual(0.06187069085946604, median, 1e-6);
Assert.AreEqual(0.06070354581334864, p025, 1e-6);
Assert.AreEqual(0.0630517079399996, p975, 1e-6);
Assert.AreEqual("B(x; α = 10008, β = 151744)", str);
}
public void BetaMeanTest3()
{
int trials = 100;
int successes = 78;
BetaDistribution betaDistribution = new BetaDistribution(successes, trials);
double mean = betaDistribution.Mean; // 0.77450980392156865
double median = betaDistribution.Median; // 0.77630912598534851
double p025 = betaDistribution.InverseDistributionFunction(p: 0.025); // 0.68899653915764347
double p975 = betaDistribution.InverseDistributionFunction(p: 0.975); // 0.84983461640764513
double orig025 = betaDistribution.DistributionFunction(p025);
double orig975 = betaDistribution.DistributionFunction(p975);
Assert.AreEqual(0.025, orig025, 1e-8);
Assert.AreEqual(0.975, orig975, 1e-8);
Assert.AreEqual(0.77450980392156865, mean, 1e-9);
Assert.AreEqual(0.7763091275412235, median, 1e-9);
Assert.AreEqual(0.68899667463246894, p025, 1e-6);
Assert.AreEqual(0.84983461640764513, p975, 1e-6);
}
