public void MaritzJarrettConfidenceIntervalWeighedTest1()
{
var random = new Random(42);
var distribution = new BetaDistribution(2, 10);
double[] data = distribution.Random(random).Next(10);
var sample1 = new Sample(data);
var sample2 = new Sample(data, new ConstantSequence(1).GenerateArray(data.Length));
var sample3 = new Sample(
data.Concat(new[] { 10.0, 10.0, 10.0 }).ToArray(),
new ConstantSequence(1).GenerateArray(data.Length).Concat(new[] { 0.0, 0.0, 0.0 }).ToArray()
);
var estimator = HarrellDavisQuantileEstimator.Instance;
var probability = Probability.Half;
var level = ConfidenceLevel.L90;
var ci1 = estimator.GetQuantileConfidenceIntervalEstimator(sample1, probability).GetConfidenceInterval(level);
var ci2 = estimator.GetQuantileConfidenceIntervalEstimator(sample2, probability).GetConfidenceInterval(level);
var ci3 = estimator.GetQuantileConfidenceIntervalEstimator(sample3, probability).GetConfidenceInterval(level);
Output.WriteLine("CI1: " + ci1.ToString("N9"));
Output.WriteLine("CI2: " + ci2.ToString("N9"));
Output.WriteLine("CI3: " + ci3.ToString("N9"));
var comparer = new AbsoluteEqualityComparer(1e-9);
Assert.True(ci1.Equals(ci2, comparer));
Assert.True(ci1.Equals(ci3, comparer));
}
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 HarrellDavisQuantileEstimatorWeightedTest1()
{
var random = new Random(42);
var distribution = new BetaDistribution(2, 10);
double[] data1 = distribution.Random(random).Next(10);
double[] data2 = data1.Select(x => x + 100).ToArray();
double[] data = data1.Concat(data2).ToArray();
var samples = new List <Sample> {
new Sample(data1)
};
for (int i = 1; i <= 40; i++)
{
samples.Add(new Sample(data, ExponentialDecaySequence.CreateFromHalfLife(i).GenerateArray(data.Length)));
}
samples.Add(new Sample(data));
var medians = samples.Select(s => HarrellDavisQuantileEstimator.Instance.GetMedian(s)).ToList();
for (int i = 0; i < medians.Count; i++)
{
Output.WriteLine($"Median[{i}] = {medians[i]:N9}");
}
for (int i = 0; i < medians.Count - 1; i++)
{
Assert.True(medians[i] < medians[i + 1]);
}
}
public async Task YeetItem([Remainder] string item)
{
var avatar = EntityConverter.ConvertUser(Context.User);
var factory = new PlayerFighterFactory();
var p = factory.CreatePlayerFighter(avatar);
var inv = avatar.Inv;
var embed = new EmbedBuilder();
var it = inv.GetItem(item);
if (inv.Remove(item))
{
UserAccountProvider.StoreUser(avatar);
var maxdist = p.Stats.Atk * Math.Sqrt(p.Stats.Spd) / Math.Log(Math.Max(it.Price / 2, 2)) / 6;
var level = Math.Min(avatar.LevelNumber, 100);
var a = 5 + (double)level / 2;
var b = 55 - (double)level / 2;
var beta = new BetaDistribution(a, b);
embed.WithDescription(
$"{Context.User.Username} yeets {it.Icon}{it.Name} {Math.Round(beta.Generate(1).FirstOrDefault() * maxdist, 2)} meters away.");
embed.WithColor(it.Color);
_ = Context.Channel.SendMessageAsync("", false, embed.Build());
}
else
{
embed.WithDescription(":x: You can only get rid of unequipped items in your possession.");
embed.WithColor(Colors.Get("Error"));
_ = Context.Channel.SendMessageAsync("", false, embed.Build());
}
await Task.CompletedTask;
}
public void BetaMLEFitTest1()
{
double[] x = samples;
{
BetaDistribution target = new BetaDistribution(0, 1);
var options = new BetaOptions()
{
Method = BetaEstimationMethod.Moments
};
target.Fit(x, options);
Assert.AreEqual(1, target.Alpha, 0.04);
Assert.AreEqual(3, target.Beta, 0.5);
}
{
BetaDistribution target = new BetaDistribution(0, 1);
var options = new BetaOptions()
{
Method = BetaEstimationMethod.MaximumLikelihood
};
target.Fit(x, options);
Assert.AreEqual(1, target.Alpha, 0.04);
Assert.AreEqual(3, target.Beta, 0.55);
}
}
public void MaritzJarrettConfidenceIntervalTest(double confidenceLevel, double minSuccessRate, double maxSuccessRate)
{
var random = new Random(42);
var distribution = new BetaDistribution(2, 10);
var generator = new LimitedRandomGenerator(distribution.Random(random).Next(1000), random);
var estimator = HarrellDavisQuantileEstimator.Instance;
double median = distribution.Median;
const int iterations = 1000;
for (int n = 5; n <= 10; n++)
{
int successCount = 0;
for (int i = 0; i < iterations; i++)
{
var sample = generator.Next(n).ToSample();
var confidenceInterval = estimator
.GetQuantileConfidenceIntervalEstimator(sample, 0.5)
.GetConfidenceInterval(confidenceLevel);
if (confidenceInterval.Contains(median))
{
successCount++;
}
}
double successRate = successCount * 1.0 / iterations;
Output.WriteLine($"n = {n}, successRate = {successRate:N4}");
Assert.True(minSuccessRate <= successRate && successRate <= maxSuccessRate);
}
}
//End of ui.cs file Contents
//-------------------------------------------------------------------------
//Begin of Random.cs file contents
/// <summary>
/// Initializes the random-number generator with a specific seed.
/// </summary>
public void Initialize(uint seed)
{
RandomNumberGenerator = new MT19937Generator(seed);
betaDist = new BetaDistribution(RandomNumberGenerator);
betaPrimeDist = new BetaPrimeDistribution(RandomNumberGenerator);
cauchyDist = new CauchyDistribution(RandomNumberGenerator);
chiDist = new ChiDistribution(RandomNumberGenerator);
chiSquareDist = new ChiSquareDistribution(RandomNumberGenerator);
continuousUniformDist = new ContinuousUniformDistribution(RandomNumberGenerator);
erlangDist = new ErlangDistribution(RandomNumberGenerator);
exponentialDist = new ExponentialDistribution(RandomNumberGenerator);
fisherSnedecorDist = new FisherSnedecorDistribution(RandomNumberGenerator);
fisherTippettDist = new FisherTippettDistribution(RandomNumberGenerator);
gammaDist = new GammaDistribution(RandomNumberGenerator);
laplaceDist = new LaplaceDistribution(RandomNumberGenerator);
lognormalDist = new LognormalDistribution(RandomNumberGenerator);
normalDist = new NormalDistribution(RandomNumberGenerator);
paretoDist = new ParetoDistribution(RandomNumberGenerator);
powerDist = new PowerDistribution(RandomNumberGenerator);
rayleighDist = new RayleighDistribution(RandomNumberGenerator);
studentsTDist = new StudentsTDistribution(RandomNumberGenerator);
triangularDist = new TriangularDistribution(RandomNumberGenerator);
weibullDist = new WeibullDistribution(RandomNumberGenerator);
poissonDist = new PoissonDistribution(RandomNumberGenerator);
// generator.randomGenerator = new MT19937Generator(seed);
}
private void GenerateIndividual_Click(object sender, RoutedEventArgs e)
{
var xCount = int.Parse(XCountRandom.Text);
var alternativesCount = int.Parse(AltCountRandom.Text);
var constraintsCount = int.Parse(ConstraintCountRandom.Text);
var optDirection = OptDirectionComboBoxRandom.SelectedIndex == 0 ? "max" : "min";
var distributionTypeIndex = DistributionType.SelectedIndex;
CustomDistribution distribution;
switch (distributionTypeIndex)
{
case 0: distribution = new BetaDistribution(double.Parse(BetaA.Text), double.Parse(BetaB.Text)); break;
case 1: distribution = new ChiDistribution(int.Parse(ChiK.Text)); break;
case 2: distribution = new GammaDistribution(double.Parse(GammaShape.Text), double.Parse(GammaRate.Text)); break;
case 3: distribution = new NormalDistribution(double.Parse(NormalMean.Text), double.Parse(NormalStdDev.Text)); break;
case 4: distribution = new UniformDistribution(double.Parse(UniformMin.Text), double.Parse(UniformMax.Text)); break;
default: distribution = new NormalDistribution(double.Parse(NormalMean.Text), double.Parse(NormalStdDev.Text)); break;
}
_viewModel.GenerateIndividualProblem(xCount, alternativesCount, constraintsCount, optDirection, distribution);
ResultsSaveStackPanel.Visibility = Visibility.Visible;
}
public void BetaInversion()
{
// test that beta distribution is accurately inverted over a wide range of a, b, P
foreach (double a in TestUtilities.GenerateRealValues(0.01, 100.0, 8))
{
foreach (double b in cs)
{
BetaDistribution B = new BetaDistribution(a, b);
foreach (double P in probabilities)
{
Console.WriteLine("a={0} b={1} P={2}", a, b, P);
double x = B.InverseLeftProbability(P);
Console.WriteLine(" x={0} P(x)={1}", x, B.LeftProbability(x));
// we would like to test that P(x) = P, but floating point limitations prevent us from meeting this standard
// P(x) changes so fast at extremes that sometimes even the minimal change in x causes a change
// in P(x) larger than our target precision; so instead we test that our routine gets us
// as close as it can, by checking that P(x-e) < P < P(x+e)
double Px = B.LeftProbability(x);
double Pxm = B.LeftProbability(Math.Min(0.0, x * (1.0 - TestUtilities.TargetPrecision)));
double Pxp = B.LeftProbability(Math.Max(x * (1.0 + TestUtilities.TargetPrecision), 1.0));
Assert.IsTrue((Pxm <= P) && (P <= Pxp));
}
}
}
}
public void BetaDistributionConstructorTest()
{
double expected, actual;
{
BetaDistribution target = new BetaDistribution(1.73, 4.2);
actual = target.ProbabilityDensityFunction(-1);
expected = 0;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(0);
expected = 0;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(1);
expected = 0;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(0.2);
expected = 2.27095841;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
actual = target.ProbabilityDensityFunction(0.4);
expected = 1.50022749;
Assert.AreEqual(expected, actual, 1e-7);
Assert.IsFalse(Double.IsNaN(actual));
}
}
public void TestBivariateRegression()
{
// Do a bunch of linear regressions. r^2 should be distributed as expected.
double a0 = 1.0;
double b0 = 0.0;
Random rng = new Random(1001110000);
ContinuousDistribution xDistribution = new UniformDistribution(Interval.FromEndpoints(-2.0, 4.0));
ContinuousDistribution eDistribution = new NormalDistribution();
List <double> r2Sample = new List <double>();
for (int i = 0; i < 500; i++)
{
BivariateSample xySample = new BivariateSample();
for (int k = 0; k < 10; k++)
{
double x = xDistribution.GetRandomValue(rng);
double y = a0 + b0 * x + eDistribution.GetRandomValue(rng);
xySample.Add(x, y);
}
LinearRegressionResult fit = xySample.LinearRegression();
double a = fit.Intercept.Value;
double b = fit.Slope.Value;
r2Sample.Add(fit.RSquared);
}
ContinuousDistribution r2Distribution = new BetaDistribution((2 - 1) / 2.0, (10 - 2) / 2.0);
TestResult ks = r2Sample.KolmogorovSmirnovTest(r2Distribution);
Assert.IsTrue(ks.Probability > 0.05);
}
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 TestBetaRoundTrip()
{
// arrange
var expected = new BetaDistribution(0.5, 0.5, 0.3, 0.7);
// act
var serialized = expected.ToString();
var deserialized = Distribution.DeserializeDistribution(serialized);
var distribution = deserialized.IfNone(() => { Assert.Fail(); return(default !); });
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 void BetaFitTest1()
{
double[] x = { 0.1, 0.5, 0.3, 0.8, 0.6, 0.7, 0.9, 0.9, 0.9, 0.9 };
BetaDistribution target = new BetaDistribution(0, 1);
target.Fit(x);
Assert.AreEqual(1.1810718232044195, target.Alpha);
Assert.AreEqual(0.60843093922651903, target.Beta);
}
public void TestBetaWithBoundsGetSample()
{
// arrange
var subject = new BetaDistribution(0.5, 0.5, 0.3, 0.7);
// act
var sample = subject.GetSample();
// assert
Assert.IsTrue(sample > 0.3 && sample < 0.7);
}
// Start is called before the first frame update
void Start()
{
rnd = new System.Random();
betaDistribution = new BetaDistribution();
bandits = new Bandit[numberOfBandits];
for (int i = 0; i < numberOfBandits; i++)
{
bandits[i] = new Bandit(rnd.NextDouble());
}
}
public void BetaFit_IntWeights()
{
double[] x = { 1.0, 0.1, 0.5, 0.3, 0.5, 0.8, 0.6, 0.7, 0.9, 0.9, 0.9 };
int[] w = { 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2 };
BetaDistribution target = new BetaDistribution(0, 1);
target.Fit(x, w);
Assert.AreEqual(1.1810718232044195, target.Alpha);
Assert.AreEqual(0.60843093922651903, target.Beta, 1e-8);
}
public void TestBetaWithBoundsFillSamples()
{
// arrange
var subject = new BetaDistribution(0.5, 0.5, 0.3, 0.7);
var samples = Range(0, 42).Map(_ => NaN).ToArray();
// act
subject.FillSamples(samples);
// assert
Assert.IsTrue(samples.All(d => d > 0.3 && d < 0.7));
}
public void BetaFit_RealWeights()
{
double[] x = { 1.0, 0.1, 0.5, 0.3, 0.5, 0.8, 0.6, 0.7, 0.9, 0.9, 0.9 };
int[] w = { 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2 };
BetaDistribution target = new BetaDistribution(0, 1);
target.Fit(x, w.ToDouble());
Assert.AreEqual(1.1401591160220996, target.Alpha);
Assert.AreEqual(0.58735469613259694, target.Beta);
}
public void TestMultivariateRegression()
{
double cz = 1.0;
double cx = 0.0;
double cy = 0.0;
Random rng = new Random(1001110000);
Distribution xDistribution = new UniformDistribution(Interval.FromEndpoints(-4.0, 8.0));
Distribution yDistribution = new UniformDistribution(Interval.FromEndpoints(-8.0, 4.0));
Distribution eDistribution = new NormalDistribution();
Sample r2Sample = new Sample();
for (int i = 0; i < 500; i++)
{
MultivariateSample xyzSample = new MultivariateSample(3);
for (int k = 0; k < 12; k++)
{
double x = xDistribution.GetRandomValue(rng);
double y = yDistribution.GetRandomValue(rng);
double z = cx * x + cy * y + cz + eDistribution.GetRandomValue(rng);
xyzSample.Add(x, y, z);
}
FitResult fit = xyzSample.LinearRegression(2);
double fcx = fit.Parameters[0];
double fcy = fit.Parameters[1];
double fcz = fit.Parameters[2];
double ss2 = 0.0;
double ss1 = 0.0;
foreach (double[] xyz in xyzSample)
{
ss2 += MoreMath.Sqr(xyz[2] - (fcx * xyz[0] + fcy * xyz[1] + fcz));
ss1 += MoreMath.Sqr(xyz[2] - xyzSample.Column(2).Mean);
}
double r2 = 1.0 - ss2 / ss1;
r2Sample.Add(r2);
}
Console.WriteLine("{0} {1} {2} {3} {4}", r2Sample.Count, r2Sample.PopulationMean, r2Sample.StandardDeviation, r2Sample.Minimum, r2Sample.Maximum);
Distribution r2Distribution = new BetaDistribution((3 - 1) / 2.0, (12 - 3) / 2.0);
//Distribution r2Distribution = new BetaDistribution((10 - 2) / 2.0, (2 - 1) / 2.0);
Console.WriteLine("{0} {1}", r2Distribution.Mean, r2Distribution.StandardDeviation);
TestResult ks = r2Sample.KolmogorovSmirnovTest(r2Distribution);
Console.WriteLine(ks.RightProbability);
Console.WriteLine(ks.Probability);
}
public async Task TestBetaCumulativeDistributionAtBounds()
{
// arrange
var subject = new BetaDistribution(0.5, 0.5, 0.3, 0.7);
var expectedLowerP = (await GetNumDataAsync("pbeta(0.3, 0.5, 0.5)"))[0].Data[0];
var expectedUpperP = (await GetNumDataAsync("pbeta(0.7, 0.5, 0.5)"))[0].Data[0];
// act
var(actualLowerP, actualUpperP) = subject.CumulativeDistributionAtBounds;
// assert
Assert.AreEqual(expectedLowerP, actualLowerP, Base.Constant.TOLERANCE);
Assert.AreEqual(expectedUpperP, actualUpperP, Base.Constant.TOLERANCE);
}
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 async Task TestBetaGetDensities()
{
// arrange
var subject = new BetaDistribution(0.5, 0.5);
var expected = (await GetNumDataAsync(
"sapply(seq(qbeta(0.3, 0.5, 0.5), qbeta(0.7, 0.5, 0.5), length.out = 5), function(cd){dbeta(cd, 0.5, 0.5)})"
))[0].Data.ToArr();
// act
var(_, actual) = subject.GetDensities(0.3, 0.7, 5);
// assert
Assert.IsTrue(actual.Count == 5);
expected.Iter((i, d) => Assert.AreEqual(d, actual[i], Base.Constant.TOLERANCE));
}
protected override void EndProcessing()
{
BetaDistribution dist;
if (ParameterSetName == "Alpha")
{
dist = new BetaDistribution(Alpha, Beta);
}
else
{
dist = new BetaDistribution(Successes, Trials);
}
var obj = DistributionHelper.AddConvinienceMethods(dist);
WriteObject(obj);
}
public void BetaGenerateTest()
{
Accord.Math.Tools.SetupGenerator(0);
int n = 100000;
double[] samples = BetaDistribution
.Random(alpha: 2, beta: 3, samples: n);
Assert.AreEqual(n, samples.Length);
var actual = BetaDistribution.Estimate(samples);
Assert.AreEqual(2, actual.Alpha, 1e-2);
Assert.AreEqual(3, actual.Beta, 1e-2);
}
public void LogLikelihoodTest()
{
var target = new BetaDistribution(3.0, 2.0);
double sum = 0;
for (int i = 0; i < samples.Length; i++)
{
sum -= target.LogProbabilityDensityFunction(samples[i]);
}
double expected = sum;
double actual = BetaDistribution.LogLikelihood(samples, target.Alpha, target.Beta);
Assert.AreEqual(expected, actual, 1e-10);
}
public void TestBivariateRegression()
{
double a0 = 1.0;
double b0 = 0.0;
Random rng = new Random(1001110000);
Distribution xDistribution = new UniformDistribution(Interval.FromEndpoints(-2.0, 4.0));
Distribution eDistribution = new NormalDistribution();
Sample r2Sample = new Sample();
for (int i = 0; i < 500; i++)
{
BivariateSample xySample = new BivariateSample();
for (int k = 0; k < 10; k++)
{
double x = xDistribution.GetRandomValue(rng);
double y = a0 + b0 * x + eDistribution.GetRandomValue(rng);
xySample.Add(x, y);
}
FitResult fit = xySample.LinearRegression();
double a = fit.Parameters[0];
double b = fit.Parameters[1];
double ss2 = 0.0;
double ss1 = 0.0;
foreach (XY xy in xySample)
{
ss2 += MoreMath.Sqr(xy.Y - (a + b * xy.X));
ss1 += MoreMath.Sqr(xy.Y - xySample.Y.Mean);
}
double r2 = 1.0 - ss2 / ss1;
r2Sample.Add(r2);
}
Console.WriteLine("{0} {1} {2} {3} {4}", r2Sample.Count, r2Sample.PopulationMean, r2Sample.StandardDeviation, r2Sample.Minimum, r2Sample.Maximum);
Distribution r2Distribution = new BetaDistribution((2 - 1) / 2.0, (10 - 2) / 2.0);
//Distribution r2Distribution = new BetaDistribution((10 - 2) / 2.0, (2 - 1) / 2.0);
Console.WriteLine("{0} {1}", r2Distribution.Mean, r2Distribution.StandardDeviation);
TestResult ks = r2Sample.KolmogorovSmirnovTest(r2Distribution);
Console.WriteLine(ks.RightProbability);
Console.WriteLine(ks.Probability);
}
public void TestBetaDistribution()
{
double[][] para =
{
new double[] { 2.5, 3.5, 0.2739037303169420423172000, 1.749247541974141744140178, 0.7393662913208028693203748, 0.5988730468534031966438193 }
};
for (int i = 0; i < para.Length; i++)
{
var tester = new ContDistTester(para[i], delegate(double a, double b)
{
var ret = new BetaDistribution(a, b);
return(ret);
}
);
tester.Test(1E-14);
}
}
public void BetaMLEFit_IntWeights()
{
double[] x = { 1.0, 0.1, 0.5, 0.3, 0.5, 0.8, 0.6, 0.7, 0.9, 0.9, 0.9 };
int[] w = { 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2 };
BetaDistribution target = new BetaDistribution(0, 1);
var options = new BetaOptions()
{
Method = BetaEstimationMethod.MaximumLikelihood
};
target.Fit(x, w, options);
Assert.AreEqual(1.1810718232044195, target.Alpha);
Assert.AreEqual(0.60843093922651903, target.Beta, 1e-10);
}
/* public Distribution(
DistributionType name,
double value1,
double value2
)
{
this.name = name;
this.value1 = value1;
this.value2 = value2;
}*/
//---------------------------------------------------------------------
public static double GenerateRandomNum(DistributionType dist, double parameter1, double parameter2)
{
double randomNum = 0.0;
/*if(dist == DistributionType.Normal)
{
NormalDistribution randVar = new NormalDistribution(RandomNumberGenerator.Singleton);
randVar.Mu = parameter1; // mean
randVar.Sigma = parameter2; // std dev
randomNum = randVar.NextDouble();
}
if(dist == DistributionType.Lognormal)
{
LognormalDistribution randVar = new LognormalDistribution(RandomNumberGenerator.Singleton);
randVar.Mu = parameter1; // mean
randVar.Sigma = parameter2; // std dev
randomNum = randVar.NextDouble();
}*/
if(dist == DistributionType.Weibull)
{
WeibullDistribution randVar = new WeibullDistribution(RandomNumberGenerator.Singleton);
randVar.Alpha = parameter1; // mean
randVar.Lambda = parameter2; // std dev
randomNum = randVar.NextDouble();
}
if(dist == DistributionType.Gamma)
{
GammaDistribution randVar = new GammaDistribution(RandomNumberGenerator.Singleton);
randVar.Alpha = parameter1; // mean
randVar.Theta = parameter2; // std dev
randomNum = randVar.NextDouble();
}
if(dist == DistributionType.Beta)
{
BetaDistribution randVar = new BetaDistribution(RandomNumberGenerator.Singleton);
randVar.Alpha = parameter1; // mean
randVar.Beta = parameter2; // std dev
randomNum = randVar.NextDouble();
}
return randomNum;
}
/// <summary>
/// Returns a new line chart plotting the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
public static ChartControl ToChart( BetaDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
ChartControl chart = GetDefaultChart();
Update( ref chart, dist, function, numInterpolatedValues );
return chart;
}
/// <summary>
/// Updates the given chart with the specified distribution.
/// </summary>
/// <param name="chart">A chart.</param>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <returns>A new chart.</returns>
/// <remarks>
/// Plots the specified function of the given distribution for 0.0001 <= p <= 0.9999.
/// <br/>
/// Titles are added only if chart does not currently contain any titles.
/// <br/>
/// chart.Series[0] is replaced, or added if necessary.
/// </remarks>
public static void Update( ref ChartControl chart, BetaDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
List<string> titles = new List<string>()
{
"BetaDistribution",
String.Format("\u03B1={0}, \u03B2={1}", dist.Alpha, dist.Beta)
};
UpdateContinuousDistribution( ref chart, dist, titles, function, numInterpolatedValues );
}
/// <summary>
/// Shows a new chart in a default form.
/// </summary>
/// <param name="dist">The distribution.</param>
/// <param name="function">The distribution function to plot.</param>
/// <param name="numInterpolatedValues">The number of interpolated values.</param>
/// <remarks>
/// Equivalent to:
/// <code>
/// NMathStatsChart.Show( ToChart( dist, function, numInterpolatedValues ) );
/// </code>
/// </remarks>
public static void Show( BetaDistribution dist, DistributionFunction function = DistributionFunction.PDF, int numInterpolatedValues = 100 )
{
Show( ToChart( dist, function, numInterpolatedValues ) );
}
