/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Laplace_distribution">Laplace distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Laplace distribution class with parameters Location = {0}, Scale = {1}
var laplace = new Laplace(0, 1);
Console.WriteLine(@"1. Initialize the new instance of the Laplace distribution class with parameters Location = {0}, Scale = {1}", laplace.Location, laplace.Scale);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", laplace);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", laplace.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", laplace.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", laplace.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", laplace.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", laplace.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", laplace.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", laplace.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", laplace.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", laplace.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", laplace.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", laplace.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", laplace.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Laplace distribution
Console.WriteLine(@"3. Generate 10 samples of the Laplace distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(laplace.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Laplace(0, 1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Laplace(0, 1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = laplace.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Laplace(0, 4) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Laplace(0, 4) distribution and display histogram");
data = new double[100000];
laplace.Scale = 4;
for (var i = 0; i < data.Length; i++)
{
data[i] = laplace.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Laplace(-10, 4) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Laplace(-10 4) distribution and display histogram");
laplace.Location = -10;
for (var i = 0; i < data.Length; i++)
{
data[i] = laplace.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateDensity(double location, double scale, double x)
{
var n = new Laplace(location, scale);
double expected = Math.Exp(-Math.Abs(x - location)/scale)/(2.0*scale);
Assert.AreEqual(expected, n.Density(x));
Assert.AreEqual(expected, Laplace.PDF(location, scale, x));
}
