public void ValidateCumulativeDistribution(double a, double b, double x, double p)
{
var dist = new Beta(a, b);
Assert.That(dist.CumulativeDistribution(x), Is.EqualTo(p).Within(1e-13));
Assert.That(Beta.CDF(a, b, x), Is.EqualTo(p).Within(1e-13));
}
public void ValidateCumulativeDistribution(double a, double b, double x, double cdf)
{
var n = new Beta(a, b);
AssertHelpers.AlmostEqual(cdf, n.CumulativeDistribution(x), 13);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Beta_distribution">Beta distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Beta distribution class with parameters a = 5 and b = 1.
var beta = new Beta(5, 1);
Console.WriteLine(@"1. Initialize the new instance of the Beta distribution class with parameters a = {0} and b = {1}", beta.A, beta.B);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", beta);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", beta.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", beta.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", beta.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", beta.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", beta.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", beta.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", beta.Mean.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", beta.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", beta.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", beta.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", beta.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Beta distribution
Console.WriteLine(@"3. Generate 10 samples of the Beta distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(beta.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Beta(5, 1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Beta(5, 1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = beta.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Beta(2, 5) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Beta(2, 5) distribution and display histogram");
beta.A = 2;
beta.B = 5;
for (var i = 0; i < data.Length; i++)
{
data[i] = beta.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Beta distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Beta(0.5, 0.5) distribution and display histogram");
beta.A = 0.5;
beta.B = 0.5;
for (var i = 0; i < data.Length; i++)
{
data[i] = beta.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 7. Generate 100000 samples of the Beta distribution and display histogram
Console.WriteLine(@"7. Generate 100000 samples of the Beta(2, 2) distribution and display histogram");
beta.A = 2;
beta.B = 2;
for (var i = 0; i < data.Length; i++)
{
data[i] = beta.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
