public void ValidateCumulativeDistribution(double location, double scale, double x)
{
var n = new Laplace(location, scale);
double expected = 0.5 * (1.0 + (Math.Sign(x - location) * (1.0 - Math.Exp(-Math.Abs(x - location) / scale))));
Assert.AreEqual(expected, n.CumulativeDistribution(x));
Assert.AreEqual(expected, Laplace.CDF(location, scale, x));
}
public void ValidateCumulativeDistribution(
[Values(0.0, 1.0, -1.0, 5.0, -5.0, Double.PositiveInfinity, Double.NegativeInfinity, 0.0, 1.0, -1.0, 5.0, -5.0, Double.PositiveInfinity, Double.NegativeInfinity, 0.0, 1.0, -1.0, 5.0, -5.0, Double.PositiveInfinity, Double.NegativeInfinity)] double location,
[Values(0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double scale,
[Values(1.5, 2.8, -5.4, -4.9, 2.0, 5.5, -0.0, Double.PositiveInfinity, 5.0, -1.0, -1.0, 2.5, 2.0, 15.0, 89.3, -0.1, 0.1, -6.1, -10.0, 2.0, -5.1)] double x)
{
var n = new Laplace(location, scale);
Assert.AreEqual(0.5 * (1.0 + (Math.Sign(x - location) * (1.0 - Math.Exp(-Math.Abs(x - location) / scale)))), n.CumulativeDistribution(x));
}
public void ValidateCumulativeDistribution(
[Values(0.0, 1.0, -1.0, 5.0, -5.0, Double.PositiveInfinity, Double.NegativeInfinity, 0.0, 1.0, -1.0, 5.0, -5.0, Double.PositiveInfinity, Double.NegativeInfinity, 0.0, 1.0, -1.0, 5.0, -5.0, Double.PositiveInfinity, Double.NegativeInfinity)] double location,
[Values(0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity, Double.PositiveInfinity)] double scale,
[Values(1.5, 2.8, -5.4, -4.9, 2.0, 5.5, -0.0, Double.PositiveInfinity, 5.0, -1.0, -1.0, 2.5, 2.0, 15.0, 89.3, -0.1, 0.1, -6.1, -10.0, 2.0, -5.1)] double x)
{
var n = new Laplace(location, scale);
Assert.AreEqual(0.5 * (1.0 + (Math.Sign(x - location) * (1.0 - Math.Exp(-Math.Abs(x - location) / scale)))), n.CumulativeDistribution(x));
}
/// <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 ValidateCumulativeDistribution(double location, double scale, double x)
{
var n = new Laplace(location, scale);
Assert.AreEqual(0.5 * (1.0 + (Math.Sign(x - location) * (1.0 - Math.Exp(-Math.Abs(x - location) / scale)))), n.CumulativeDistribution(x));
}
public void ValidateCumulativeDistribution(double location, double scale, double x)
{
var n = new Laplace(location, scale);
Assert.AreEqual <double>(0.5 * (1.0 + Math.Sign(x - location) * (1.0 - Math.Exp(-Math.Abs(x - location) / scale))), n.CumulativeDistribution(x));
}