/// <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 ValidateProbability(double r, double p, int x)
{
var d = new NegativeBinomial(r, p);
Assert.AreEqual(Math.Exp(SpecialFunctions.GammaLn(r + x) - SpecialFunctions.GammaLn(r) - SpecialFunctions.GammaLn(x + 1.0) + (r * Math.Log(p)) + (x * Math.Log(1.0 - p))), d.Probability(x));
}