/// <summary>
/// Run example
/// </summary>
public void Run()
{
// 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform distribution on [-10, 10]
var uniform = new ContinuousUniform(-10, 10);
var result = Generate.RandomMap(10, uniform, Function);
Console.WriteLine(@" 1. Get 10 random samples of f(x) = (x * x) / 2 using continuous uniform distribution on [-10, 10]");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution and retrieve sample points
var exponential = new Exponential(1);
double[] samplePoints = Generate.Random(10, exponential);
result = Generate.Map(samplePoints, Function);
Console.WriteLine(@"2. Get 10 random samples of f(x) = (x * x) / 2 using Exponential(1) distribution and retrieve sample points");
Console.Write(@"Points: ");
for (var i = 0; i < samplePoints.Length; i++)
{
Console.Write(samplePoints[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.Write(@"Values: ");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution
var chiSquare = new ChiSquared(10);
result = Generate.RandomMap2(10, chiSquare, TwoDomainFunction);
Console.WriteLine(@" 3. Get 10 random samples of f(x, y) = (x * y) / 2 using ChiSquare(10) distribution");
for (var i = 0; i < result.Length; i++)
{
Console.Write(result[i].ToString("N") + @" ");
}
Console.WriteLine();
}
public void CanSample()
{
var n = new Exponential(1.0);
n.Sample();
}
public void ValidateDensityLn(double lambda, double x)
{
var n = new Exponential(lambda);
Assert.AreEqual(Math.Log(lambda) - (lambda*x), n.DensityLn(x));
Assert.AreEqual(Math.Log(lambda) - (lambda*x), Exponential.PDFLn(lambda, x));
}
public void ValidateDensity(double lambda, double x)
{
var n = new Exponential(lambda);
if (x >= 0)
{
Assert.AreEqual(lambda*Math.Exp(-lambda*x), n.Density(x));
Assert.AreEqual(lambda*Math.Exp(-lambda*x), Exponential.PDF(lambda, x));
}
else
{
Assert.AreEqual(0.0, n.Density(lambda));
Assert.AreEqual(0.0, Exponential.PDF(lambda, lambda));
}
}
public void ValidateMaximum()
{
var n = new Exponential(1.0);
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Exponential_distribution">Exponential distribution</a>
public void Run()
{
// 1. Initialize the new instance of the Exponential distribution class with parameter Lambda = 1.
var exponential = new Exponential(1);
Console.WriteLine(@"1. Initialize the new instance of the Exponential distribution class with parameter Lambda = {0}", exponential.Lambda);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", exponential);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", exponential.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", exponential.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", exponential.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", exponential.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", exponential.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", exponential.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", exponential.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", exponential.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", exponential.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", exponential.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", exponential.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", exponential.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples of the Exponential distribution
Console.WriteLine(@"3. Generate 10 samples of the Exponential distribution");
for (var i = 0; i < 10; i++)
{
Console.Write(exponential.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the Exponential(1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the Exponential(1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = exponential.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the Exponential(9) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the Exponential(9) distribution and display histogram");
exponential.Lambda = 9;
for (var i = 0; i < data.Length; i++)
{
data[i] = exponential.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the Exponential(0.01) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the Exponential(0.01) distribution and display histogram");
exponential.Lambda = 0.01;
for (var i = 0; i < data.Length; i++)
{
data[i] = exponential.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateToString()
{
var n = new Exponential(2d);
Assert.AreEqual("Exponential(λ = 2)", n.ToString());
}
public void ValidateInverseCumulativeDistribution(double lambda, double x)
{
var n = new Exponential(lambda);
Assert.AreEqual(x, n.InverseCumulativeDistribution(1.0 - Math.Exp(-lambda*x)));
Assert.AreEqual(x, Exponential.InvCDF(lambda, 1.0 - Math.Exp(-lambda*x)));
}
public void ValidateSkewness(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(2.0, n.Skewness);
}
public void ValidateEntropy(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(1.0 - Math.Log(lambda), n.Entropy);
}
public void ValidateStdDev(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(1.0 / lambda, n.StdDev);
}
public void ValidateVariance(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(1.0 / (lambda * lambda), n.Variance);
}
public void SetLambdaFailsWithNegativeLambda()
{
var n = new Exponential(1.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Rate = -1.0);
}
public void CanSampleSequence()
{
var n = new Exponential(1.0);
var ied = n.Samples();
GC.KeepAlive(ied.Take(5).ToArray());
}
public void ValidateMode(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(0.0, n.Mode);
}
public void ValidateCumulativeDistribution(double lambda, double x)
{
var n = new Exponential(lambda);
if (x >= 0.0)
{
Assert.AreEqual(1.0 - Math.Exp(-lambda*x), n.CumulativeDistribution(x));
Assert.AreEqual(1.0 - Math.Exp(-lambda*x), Exponential.CDF(lambda, x));
}
else
{
Assert.AreEqual(0.0, n.CumulativeDistribution(x));
Assert.AreEqual(0.0, Exponential.CDF(lambda, x));
}
}
public void ValidateMedian(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(Math.Log(2.0) / lambda, n.Median);
}
public void CanCreateExponential(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(lambda, n.Rate);
}
public void ValidateMinimum()
{
var n = new Exponential(1.0);
Assert.AreEqual(0.0, n.Minimum);
}
public void ValidateMean(double lambda)
{
var n = new Exponential(lambda);
Assert.AreEqual(1.0 / lambda, n.Mean);
}
public void SetLambdaFailsWithNegativeLambda()
{
var n = new Exponential(1.0);
Assert.That(() => n.Rate = -1.0, Throws.ArgumentException);
}