/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Cauchy distribution class with parameters Location = 1 and Scale = 2.
var cauchy = new Cauchy(1, 2);
Console.WriteLine(@"1. Initialize the new instance of the Cauchy distribution class with parameters Location = {0} and Scale = {1}", cauchy.Location, cauchy.Scale);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", cauchy);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", cauchy.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", cauchy.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", cauchy.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", cauchy.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", cauchy.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", cauchy.Minimum.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", cauchy.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", cauchy.Mode.ToString(" #0.00000;-#0.00000"));
// 3. Generate 10 samples of the Cauchy distribution
Console.WriteLine(@"3. Generate 10 samples of the Cauchy distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(cauchy.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
}
public void ValidateCumulativeDistribution(double location, double scale)
{
var n = new Cauchy(location, scale);
for (var i = 0; i < 11; i++)
{
var x = i - 5.0;
double expected = (Math.Atan((x - location)/scale))/Math.PI + 0.5;
Assert.AreEqual(expected, n.CumulativeDistribution(x), 1e-12);
Assert.AreEqual(expected, Cauchy.CDF(location, scale, x), 1e-12);
}
}
