public void ValidateToString()
{
System.Threading.Thread.CurrentThread.CurrentCulture = System.Globalization.CultureInfo.InvariantCulture;
var d = new NegativeBinomial(1.0, 0.3);
Assert.AreEqual(String.Format("NegativeBinomial(R = {0}, P = {1})", d.R, d.P), d.ToString());
}
public void CanSampleSequence()
{
var d = new NegativeBinomial(1.0, 0.5);
var ied = d.Samples();
ied.Take(5).ToArray();
}
public void CanCreateNegativeBinomial(double r, double p)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(r, d.R);
Assert.AreEqual(p, d.P);
}
public void CanCreateNegativeBinomial([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(r, d.R);
Assert.AreEqual(p, d.P);
}
public void ValidateMode(double r, double p)
{
var d = new NegativeBinomial(r, p);
if (r > 1)
{
Assert.AreEqual((int)Math.Floor((r - 1.0) * (1.0 - p) / p), d.Mode);
}
else
{
Assert.AreEqual(0.0, d.Mode);
}
}
public void ValidateCumulativeDistribution([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p, [Values(0, 1, 2, 3, 5)] int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.BetaRegularized(r, x + 1.0, p), d.CumulativeDistribution(x), 1e-12);
}
private static void negative_binomial_cdf_test()
//****************************************************************************80
//
// Purpose:
//
// NEGATIVE_BINOMIAL_CDF_TEST tests NEGATIVE_BINOMIAL_CDF.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 April 2016
//
// Author:
//
// John Burkardt
//
{
int i;
int seed = 123456789;
Console.WriteLine("");
Console.WriteLine("NEGATIVE_BINOMIAL_CDF_TEST");
Console.WriteLine(" NEGATIVE_BINOMIAL_CDF evaluates the Negative Binomial CDF;");
Console.WriteLine(" NEGATIVE_BINOMIAL_CDF_INV inverts the Negative Binomial CDF.");
Console.WriteLine(" NEGATIVE_BINOMIAL_PDF evaluates the Negative Binomial PDF;");
const int a = 2;
const double b = 0.25;
Console.WriteLine("");
Console.WriteLine(" PDF parameter A = " + a + "");
Console.WriteLine(" PDF parameter B = " + b + "");
if (!NegativeBinomial.negative_binomial_check(a, b))
{
Console.WriteLine("");
Console.WriteLine("NEGATIVE_BINOMIAL_CDF_TEST - Fatal error!");
Console.WriteLine(" The parameters are not legal.");
return;
}
Console.WriteLine("");
Console.WriteLine(" X PDF CDF CDF_INV");
Console.WriteLine("");
for (i = 1; i <= 10; i++)
{
int x = NegativeBinomial.negative_binomial_sample(a, b, ref seed);
double pdf = NegativeBinomial.negative_binomial_pdf(x, a, b);
double cdf = NegativeBinomial.negative_binomial_cdf(x, a, b);
int x2 = NegativeBinomial.negative_binomial_cdf_inv(cdf, a, b);
Console.WriteLine(" "
+ x.ToString(CultureInfo.InvariantCulture).PadLeft(12) + " "
+ pdf.ToString(CultureInfo.InvariantCulture).PadLeft(12) + " "
+ cdf.ToString(CultureInfo.InvariantCulture).PadLeft(12) + " "
+ x2.ToString(CultureInfo.InvariantCulture).PadLeft(12) + "");
}
}
public void ValidateProbabilityLn(double r, double p, int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.GammaLn(r + x) - SpecialFunctions.GammaLn(r) - SpecialFunctions.GammaLn(x + 1.0) + (r * Math.Log(p)) + (x * Math.Log(1.0 - p)), d.ProbabilityLn(x));
}
public void SetRFails(double r)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws <ArgumentOutOfRangeException>(() => d.R = r);
}
public void ValidateToString()
{
var d = new NegativeBinomial(1.0, 0.3);
Assert.AreEqual(String.Format("NegativeBinomial(R = {0}, P = {1})", d.R, d.P), d.ToString());
}
public void SetProbabilityOfOneFails(double p)
{
var d = new NegativeBinomial(1.0, 0.5);
d.P = p;
}
public void SetRFails(double r)
{
var d = new NegativeBinomial(1.0, 0.5);
d.R = r;
}
public void SetRFails(double r)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.That(() => d.R = r, Throws.ArgumentException);
}
public void SetProbabilityOfOneFails(double p)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.That(() => d.P = p, Throws.ArgumentException);
}
public void ValidateCumulativeDistribution([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p, [Values(0, 1, 2, 3, 5)] int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.BetaRegularized(r, x + 1.0, p), d.CumulativeDistribution(x), 1e-12);
}
public void ValidateProbabilityLn([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p, [Values(0, 1, 2, 3, 5)] int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.GammaLn(r + x) - SpecialFunctions.GammaLn(r) - SpecialFunctions.GammaLn(x + 1.0) + (r * Math.Log(p)) + (x * Math.Log(1.0 - p)), d.ProbabilityLn(x));
}
public void ValidateSkewness([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p)
{
var b = new NegativeBinomial(r, p);
Assert.AreEqual((2.0 - p) / Math.Sqrt(r * (1.0 - p)), b.Skewness);
}
public void ValidateEntropy()
{
var d = new NegativeBinomial(1.0, 0.5);
var e = d.Entropy;
}
public void ValidateProbabilityLn([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p, [Values(0, 1, 2, 3, 5)] int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.GammaLn(r + x) - SpecialFunctions.GammaLn(r) - SpecialFunctions.GammaLn(x + 1.0) + (r * Math.Log(p)) + (x * Math.Log(1.0 - p)), d.ProbabilityLn(x));
}
public void ValidateMedian()
{
var d = new NegativeBinomial(1.0, 0.5);
int m = d.Median;
}
public void CanSample()
{
var d = new NegativeBinomial(1.0, 0.5);
d.Sample();
}
public void NegativeBinomialCreateFailsWithBadParameters(double r, double p)
{
var d = new NegativeBinomial(r, p);
}
public void ValidateEntropyThrowsNotSupportedException()
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws <NotSupportedException>(() => { var e = d.Entropy; });
}
public void CanSetR(double r)
{
var d = new NegativeBinomial(1.0, 0.5);
d.R = r;
}
public void ValidateMinimum()
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.AreEqual(0, d.Minimum);
}
public void SetRFails(double r)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws<ArgumentOutOfRangeException>(() => d.R = r);
}
public void CanSample()
{
var d = new NegativeBinomial(1.0, 0.5);
d.Sample();
}
public void ValidateCumulativeDistribution(double r, double p, int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.BetaRegularized(r, x + 1.0, p), d.CumulativeDistribution(x), 1e-12);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Negative_binomial">NegativeBinomial distribution</a>
public void Run()
{
// 1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = 0.2, R = 20
var negativeBinomial = new NegativeBinomial(20, 0.2);
Console.WriteLine(@"1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = {0}, N = {1}", negativeBinomial.P, negativeBinomial.R);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", negativeBinomial);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '3'", negativeBinomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability mass at location '3'", negativeBinomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability mass at location '3'", negativeBinomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", negativeBinomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", negativeBinomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", negativeBinomial.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", negativeBinomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", negativeBinomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", negativeBinomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", negativeBinomial.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the NegativeBinomial distribution
Console.WriteLine(@"3. Generate 10 samples of the NegativeBinomial distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(negativeBinomial.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the NegativeBinomial(0.2, 20) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the NegativeBinomial(0.2, 20) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = negativeBinomial.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the NegativeBinomial(0.7, 20) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the NegativeBinomial(0.7, 20) distribution and display histogram");
negativeBinomial.P = 0.7;
for (var i = 0; i < data.Length; i++)
{
data[i] = negativeBinomial.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the NegativeBinomial(0.5, 1) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the NegativeBinomial(0.5, 1) distribution and display histogram");
negativeBinomial.P = 0.5;
negativeBinomial.R = 1;
for (var i = 0; i < data.Length; i++)
{
data[i] = negativeBinomial.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateMaximum()
{
var d = new NegativeBinomial(1.0, 0.3);
Assert.AreEqual(int.MaxValue, d.Maximum);
}
public void SetRFails([Values(Double.NaN, -1.0, Double.NegativeInfinity)] double r)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws<ArgumentOutOfRangeException>(() => d.R = r);
}
public void ValidateMinimum()
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.AreEqual(0, d.Minimum);
}
public void ValidateEntropyThrowsNotSupportedException()
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws<NotSupportedException>(() => { var e = d.Entropy; });
}
public void SetRFails([Values(Double.NaN, -1.0, Double.NegativeInfinity)] double r)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws <ArgumentOutOfRangeException>(() => d.R = r);
}
public void ValidateMedianThrowsNotSupportedException()
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws<NotSupportedException>(() => { var m = d.Median; });
}
public void NegativeBinomialCreateFailsWithBadParameters(double r, double p)
{
var d = new NegativeBinomial(r, p);
}
public void ValidateMode([Values(0.0, 0.3, 1.0)] double r, [Values(0.0, 0.0, 1.0)] double p)
{
var d = new NegativeBinomial(r, p);
if (r > 1)
{
Assert.AreEqual((int)Math.Floor((r - 1.0) * (1.0 - p) / p), d.Mode);
}
else
{
Assert.AreEqual(0.0, d.Mode);
}
}
public void SetRFails(double r)
{
var d = new NegativeBinomial(1.0, 0.5);
d.R = r;
}
public void ValidateSkewness([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p)
{
var b = new NegativeBinomial(r, p);
Assert.AreEqual((2.0 - p) / Math.Sqrt(r * (1.0 - p)), b.Skewness);
}
public void ValidateCumulativeDistribution()
{
var d = new NegativeBinomial(1.0, 0.5);
var cdx = d.CumulativeDistribution(1.5);
}
public void CanCreateNegativeBinomial([Values(0.0, 0.1, 1.0)] double r, [Values(0.0, 0.3, 1.0)] double p)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(r, d.R);
Assert.AreEqual(p, d.P);
}
public void ValidateEntropy()
{
var d = new NegativeBinomial(1.0, 0.5);
var e = d.Entropy;
}
public void CanSampleSequence()
{
var d = new NegativeBinomial(1.0, 0.5);
var ied = d.Samples();
ied.Take(5).ToArray();
}
public void ValidateMaximum()
{
var d = new NegativeBinomial(1.0, 0.3);
int max = d.Maximum;
}
public void SetProbabilityOfOneFails(double p)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws <ArgumentOutOfRangeException>(() => d.P = p);
}
public void ValidateMedian()
{
var d = new NegativeBinomial(1.0, 0.5);
int m = d.Median;
}
public void ValidateSkewness(double r, double p)
{
var b = new NegativeBinomial(r, p);
Assert.AreEqual((2.0 - p) / Math.Sqrt(r * (1.0 - p)), b.Skewness);
}
public void ValidateProbabilityLn(double r, double p, int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.GammaLn(r + x) - SpecialFunctions.GammaLn(r) - SpecialFunctions.GammaLn(x + 1.0) + r * Math.Log(p) + x * Math.Log(1.0 - p), d.ProbabilityLn(x));
}
public void ValidateMedianThrowsNotSupportedException()
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws <NotSupportedException>(() => { var m = d.Median; });
}
public void ValidateSkewness(double r, double p)
{
var b = new NegativeBinomial(r, p);
Assert.AreEqual<double>((2.0 - p) / Math.Sqrt(r * (1.0 - p)), b.Skewness);
}
public void ValidateMaximum()
{
var d = new NegativeBinomial(1.0, 0.3);
Assert.AreEqual(int.MaxValue, d.Maximum);
}
public void ValidateToString()
{
var d = new NegativeBinomial(1.0, 0.3);
Assert.AreEqual<string>("NegativeBinomial(R = 1, P = 0.3)", d.ToString());
}
public void ValidateCumulativeDistribution(double r, double p, int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(SpecialFunctions.BetaRegularized(r, x + 1.0, p), d.CumulativeDistribution(x), 1e-12);
}
public void CanCreateNegativeBinomial(double r, double p)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual<double>(r, d.R);
Assert.AreEqual<double>(p, d.P);
}
public void CanSetProbabilityOfOne(double p)
{
var d = new NegativeBinomial(1.0, 0.5);
d.P = p;
}
public void CanSetR(double r)
{
var d = new NegativeBinomial(1.0, 0.5);
d.R = r;
}
public void ValidateToString()
{
var d = new NegativeBinomial(1.0, 0.3);
Assert.AreEqual(String.Format("NegativeBinomial(R = {0}, P = {1})", d.R, d.P), d.ToString());
}
public void SetProbabilityOfOneFails([Values(Double.NaN, -1.0, 2.0)] double p)
{
var d = new NegativeBinomial(1.0, 0.5);
Assert.Throws<ArgumentOutOfRangeException>(() => d.P = p);
}
public override void ExecuteExample()
{
// <a href="http://en.wikipedia.org/wiki/Binomial_distribution">Binomial distribution</a>
MathDisplay.WriteLine("<b>Binomial distribution</b>");
// 1. Initialize the new instance of the Binomial distribution class with parameters P = 0.2, N = 20
var binomial = new Binomial(0.2, 20);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Binomial distribution class with parameters P = {0}, N = {1}", binomial.P, binomial.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomial.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomial.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomial.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", binomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", binomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Binomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Binomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Bernoulli_distribution">Bernoulli distribution</a>
MathDisplay.WriteLine("<b>Bernoulli distribution</b>");
// 1. Initialize the new instance of the Bernoulli distribution class with parameter P = 0.2
var bernoulli = new Bernoulli(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Bernoulli distribution class with parameter P = {0}", bernoulli.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", bernoulli);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", bernoulli.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", bernoulli.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", bernoulli.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", bernoulli.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", bernoulli.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", bernoulli.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", bernoulli.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", bernoulli.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", bernoulli.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", bernoulli.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", bernoulli.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Bernoulli distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Bernoulli distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(bernoulli.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Categorical_distribution">Categorical distribution</a>
MathDisplay.WriteLine("<b>Categorical distribution</b>");
// 1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)
var binomialC = new Categorical(new[] { 0.1, 0.2, 0.25, 0.45 });
MathDisplay.WriteLine(@"1. Initialize the new instance of the Categorical distribution class with parameters P = (0.1, 0.2, 0.25, 0.45)");
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", binomialC);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", binomialC.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", binomialC.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", binomialC.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", binomialC.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", binomialC.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", binomialC.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", binomialC.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", binomialC.Median.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", binomialC.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", binomialC.StdDev.ToString(" #0.00000;-#0.00000"));
// 3. Generate 10 samples of the Categorical distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Categorical distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(binomialC.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution">ConwayMaxwellPoisson distribution</a>
MathDisplay.WriteLine("<b>Conway Maxwell Poisson distribution</b>");
// 1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = 2, Nu = 1
var conwayMaxwellPoisson = new ConwayMaxwellPoisson(2, 1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the ConwayMaxwellPoisson distribution class with parameters Lambda = {0}, Nu = {1}", conwayMaxwellPoisson.Lambda, conwayMaxwellPoisson.Nu);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", conwayMaxwellPoisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", conwayMaxwellPoisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", conwayMaxwellPoisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", conwayMaxwellPoisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", conwayMaxwellPoisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", conwayMaxwellPoisson.Mean.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", conwayMaxwellPoisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", conwayMaxwellPoisson.StdDev.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the ConwayMaxwellPoisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the ConwayMaxwellPoisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(conwayMaxwellPoisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Discrete_uniform">DiscreteUniform distribution</a>
MathDisplay.WriteLine("<b>Discrete Uniform distribution</b>");
// 1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = 2, UpperBound = 10
var discreteUniform = new DiscreteUniform(2, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the DiscreteUniform distribution class with parameters LowerBound = {0}, UpperBound = {1}", discreteUniform.LowerBound, discreteUniform.UpperBound);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", discreteUniform);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", discreteUniform.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", discreteUniform.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", discreteUniform.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", discreteUniform.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", discreteUniform.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", discreteUniform.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", discreteUniform.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", discreteUniform.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", discreteUniform.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", discreteUniform.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", discreteUniform.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", discreteUniform.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the DiscreteUniform distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the DiscreteUniform distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(discreteUniform.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Geometric_distribution">Geometric distribution</a>
MathDisplay.WriteLine("<b>Geometric distribution</b>");
// 1. Initialize the new instance of the Geometric distribution class with parameter P = 0.2
var geometric = new Geometric(0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Geometric distribution class with parameter P = {0}", geometric.P);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", geometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", geometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", geometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", geometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", geometric.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", geometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", geometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", geometric.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", geometric.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", geometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", geometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", geometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", geometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Geometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Geometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(geometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Hypergeometric_distribution">Hypergeometric distribution</a>
MathDisplay.WriteLine("<b>Hypergeometric distribution</b>");
// 1. Initialize the new instance of the Hypergeometric distribution class with parameters PopulationSize = 10, M = 2, N = 8
var hypergeometric = new Hypergeometric(30, 15, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Hypergeometric distribution class with parameters Population = {0}, Success = {1}, Draws = {2}", hypergeometric.Population, hypergeometric.Success, hypergeometric.Draws);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", hypergeometric);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", hypergeometric.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", hypergeometric.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", hypergeometric.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", hypergeometric.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", hypergeometric.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", hypergeometric.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", hypergeometric.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", hypergeometric.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", hypergeometric.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", hypergeometric.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Hypergeometric distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Hypergeometric distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(hypergeometric.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Negative_binomial">NegativeBinomial distribution</a>
MathDisplay.WriteLine("<b>Negative Binomial distribution</b>");
// 1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = 0.2, R = 20
var negativeBinomial = new NegativeBinomial(20, 0.2);
MathDisplay.WriteLine(@"1. Initialize the new instance of the NegativeBinomial distribution class with parameters P = {0}, N = {1}", negativeBinomial.P, negativeBinomial.R);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", negativeBinomial);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", negativeBinomial.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", negativeBinomial.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", negativeBinomial.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", negativeBinomial.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", negativeBinomial.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", negativeBinomial.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", negativeBinomial.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", negativeBinomial.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", negativeBinomial.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", negativeBinomial.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the NegativeBinomial distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the NegativeBinomial distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(negativeBinomial.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Poisson_distribution">Poisson distribution</a>
MathDisplay.WriteLine("<b>Poisson distribution</b>");
// 1. Initialize the new instance of the Poisson distribution class with parameter Lambda = 1
var poisson = new Poisson(1);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Poisson distribution class with parameter Lambda = {0}", poisson.Lambda);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", poisson);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", poisson.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", poisson.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", poisson.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", poisson.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", poisson.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", poisson.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", poisson.Mean.ToString(" #0.00000;-#0.00000"));
// Median
MathDisplay.WriteLine(@"{0} - Median", poisson.Median.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", poisson.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", poisson.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", poisson.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", poisson.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Poisson distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Poisson distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(poisson.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
// <a href="http://en.wikipedia.org/wiki/Zipf_distribution">Zipf distribution</a>
MathDisplay.WriteLine("<b>Zipf distribution</b>");
// 1. Initialize the new instance of the Zipf distribution class with parameters S = 5, N = 10
var zipf = new Zipf(5, 10);
MathDisplay.WriteLine(@"1. Initialize the new instance of the Zipf distribution class with parameters S = {0}, N = {1}", zipf.S, zipf.N);
MathDisplay.WriteLine();
// 2. Distributuion properties:
MathDisplay.WriteLine(@"2. {0} distributuion properties:", zipf);
// Cumulative distribution function
MathDisplay.WriteLine(@"{0} - Сumulative distribution at location '3'", zipf.CumulativeDistribution(3).ToString(" #0.00000;-#0.00000"));
// Probability density
MathDisplay.WriteLine(@"{0} - Probability mass at location '3'", zipf.Probability(3).ToString(" #0.00000;-#0.00000"));
// Log probability density
MathDisplay.WriteLine(@"{0} - Log probability mass at location '3'", zipf.ProbabilityLn(3).ToString(" #0.00000;-#0.00000"));
// Entropy
MathDisplay.WriteLine(@"{0} - Entropy", zipf.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
MathDisplay.WriteLine(@"{0} - Largest element in the domain", zipf.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
MathDisplay.WriteLine(@"{0} - Smallest element in the domain", zipf.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
MathDisplay.WriteLine(@"{0} - Mean", zipf.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
MathDisplay.WriteLine(@"{0} - Mode", zipf.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
MathDisplay.WriteLine(@"{0} - Variance", zipf.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
MathDisplay.WriteLine(@"{0} - Standard deviation", zipf.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
MathDisplay.WriteLine(@"{0} - Skewness", zipf.Skewness.ToString(" #0.00000;-#0.00000"));
MathDisplay.WriteLine();
// 3. Generate 10 samples of the Zipf distribution
MathDisplay.WriteLine(@"3. Generate 10 samples of the Zipf distribution");
for (var i = 0; i < 10; i++)
{
MathDisplay.Write(zipf.Sample().ToString("N05") + @" ");
}
MathDisplay.FlushBuffer();
MathDisplay.WriteLine();
MathDisplay.WriteLine();
}
private static void negative_binomial_sample_test()
//****************************************************************************80
//
// Purpose:
//
// NEGATIVE_BINOMIAL_SAMPLE_TEST tests NEGATIVE_BINOMIAL_SAMPLE.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 03 April 2016
//
// Author:
//
// John Burkardt
//
{
const int SAMPLE_NUM = 1000;
int i;
int seed = 123456789;
int[] x = new int[SAMPLE_NUM];
Console.WriteLine("");
Console.WriteLine("NEGATIVE_BINOMIAL_SAMPLE_TEST");
Console.WriteLine(" NEGATIVE_BINOMIAL_MEAN computes the Negative Binomial mean;");
Console.WriteLine(" NEGATIVE_BINOMIAL_SAMPLE samples the Negative Binomial distribution;");
Console.WriteLine(" NEGATIVE_BINOMIAL_VARIANCE computes the Negative Binomial variance;");
const int a = 2;
const double b = 0.75;
Console.WriteLine("");
Console.WriteLine(" PDF parameter A = " + a + "");
Console.WriteLine(" PDF parameter B = " + b + "");
if (!NegativeBinomial.negative_binomial_check(a, b))
{
Console.WriteLine("");
Console.WriteLine("NEGATIVE_BINOMIAL_SAMPLE_TEST - Fatal error!");
Console.WriteLine(" The parameters are not legal.");
return;
}
double mean = NegativeBinomial.negative_binomial_mean(a, b);
double variance = NegativeBinomial.negative_binomial_variance(a, b);
Console.WriteLine("");
Console.WriteLine(" PDF mean = " + mean + "");
Console.WriteLine(" PDF variance = " + variance + "");
for (i = 0; i < SAMPLE_NUM; i++)
{
x[i] = NegativeBinomial.negative_binomial_sample(a, b, ref seed);
}
mean = typeMethods.i4vec_mean(SAMPLE_NUM, x);
variance = typeMethods.i4vec_variance(SAMPLE_NUM, x);
int xmax = typeMethods.i4vec_max(SAMPLE_NUM, x);
int xmin = typeMethods.i4vec_min(SAMPLE_NUM, x);
Console.WriteLine("");
Console.WriteLine(" Sample size = " + SAMPLE_NUM + "");
Console.WriteLine(" Sample mean = " + mean + "");
Console.WriteLine(" Sample variance = " + variance + "");
Console.WriteLine(" Sample maximum = " + xmax + "");
Console.WriteLine(" Sample minimum = " + xmin + "");
}
