public void CanEstimateParameters(double mu, double sigma)
{
var original = new LogNormal(mu, sigma, new Random(100));
var estimated = LogNormal.Estimate(original.Samples().Take(10000));
AssertHelpers.AlmostEqualRelative(mu, estimated.Mu, 1);
AssertHelpers.AlmostEqualRelative(sigma, estimated.Sigma, 1);
}
public void SetupDistributions()
{
dists = new IDistribution[8];
dists[0] = new Beta(1.0, 1.0);
dists[1] = new ContinuousUniform(0.0, 1.0);
dists[2] = new Gamma(1.0, 1.0);
dists[3] = new Normal(0.0, 1.0);
dists[4] = new Bernoulli(0.6);
dists[5] = new Weibull(1.0, 1.0);
dists[6] = new DiscreteUniform(1, 10);
dists[7] = new LogNormal(1.0, 1.0);
}
public void ValidateMean(double mu, double sigma, double mean)
{
var n = new LogNormal(mu, sigma);
AssertHelpers.AlmostEqualRelative(mean, n.Mean, 14);
}
public void ValidateMaximum()
{
var n = new LogNormal(1.0, 2.0);
Assert.AreEqual(Double.PositiveInfinity, n.Maximum);
}
public void LogNormalCreateFailsWithBadParameters(double mu, double sigma)
{
var n = new LogNormal(mu, sigma);
}
/// <summary>
/// Run example
/// </summary>
/// <a href="http://en.wikipedia.org/wiki/Log-normal_distribution">LogNormal distribution</a>
public void Run()
{
// 1. Initialize the new instance of the LogNormal distribution class with parameters Mu = 0, Sigma = 1
var logNormal = new LogNormal(0, 1);
Console.WriteLine(@"1. Initialize the new instance of the LogNormal distribution class with parameters Mu = {0}, Sigma = {1}", logNormal.Mu, logNormal.Sigma);
Console.WriteLine();
// 2. Distributuion properties:
Console.WriteLine(@"2. {0} distributuion properties:", logNormal);
// Cumulative distribution function
Console.WriteLine(@"{0} - Сumulative distribution at location '0.3'", logNormal.CumulativeDistribution(0.3).ToString(" #0.00000;-#0.00000"));
// Probability density
Console.WriteLine(@"{0} - Probability density at location '0.3'", logNormal.Density(0.3).ToString(" #0.00000;-#0.00000"));
// Log probability density
Console.WriteLine(@"{0} - Log probability density at location '0.3'", logNormal.DensityLn(0.3).ToString(" #0.00000;-#0.00000"));
// Entropy
Console.WriteLine(@"{0} - Entropy", logNormal.Entropy.ToString(" #0.00000;-#0.00000"));
// Largest element in the domain
Console.WriteLine(@"{0} - Largest element in the domain", logNormal.Maximum.ToString(" #0.00000;-#0.00000"));
// Smallest element in the domain
Console.WriteLine(@"{0} - Smallest element in the domain", logNormal.Minimum.ToString(" #0.00000;-#0.00000"));
// Mean
Console.WriteLine(@"{0} - Mean", logNormal.Mean.ToString(" #0.00000;-#0.00000"));
// Median
Console.WriteLine(@"{0} - Median", logNormal.Median.ToString(" #0.00000;-#0.00000"));
// Mode
Console.WriteLine(@"{0} - Mode", logNormal.Mode.ToString(" #0.00000;-#0.00000"));
// Variance
Console.WriteLine(@"{0} - Variance", logNormal.Variance.ToString(" #0.00000;-#0.00000"));
// Standard deviation
Console.WriteLine(@"{0} - Standard deviation", logNormal.StdDev.ToString(" #0.00000;-#0.00000"));
// Skewness
Console.WriteLine(@"{0} - Skewness", logNormal.Skewness.ToString(" #0.00000;-#0.00000"));
Console.WriteLine();
// 3. Generate 10 samples
Console.WriteLine(@"3. Generate 10 samples");
for (var i = 0; i < 10; i++)
{
Console.Write(logNormal.Sample().ToString("N05") + @" ");
}
Console.WriteLine();
Console.WriteLine();
// 4. Generate 100000 samples of the LogNormal(0, 1) distribution and display histogram
Console.WriteLine(@"4. Generate 100000 samples of the LogNormal(0, 1) distribution and display histogram");
var data = new double[100000];
for (var i = 0; i < data.Length; i++)
{
data[i] = logNormal.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 5. Generate 100000 samples of the LogNormal(0, 0.5) distribution and display histogram
Console.WriteLine(@"5. Generate 100000 samples of the LogNormal(0, 0.5) distribution and display histogram");
logNormal.Sigma = 0.5;
for (var i = 0; i < data.Length; i++)
{
data[i] = logNormal.Sample();
}
ConsoleHelper.DisplayHistogram(data);
Console.WriteLine();
// 6. Generate 100000 samples of the LogNormal(5, 0.25) distribution and display histogram
Console.WriteLine(@"6. Generate 100000 samples of the LogNormal(5, 0.25) distribution and display histogram");
logNormal.Mu = 5;
logNormal.Sigma = 0.25;
for (var i = 0; i < data.Length; i++)
{
data[i] = logNormal.Sample();
}
ConsoleHelper.DisplayHistogram(data);
}
public void ValidateToString()
{
var n = new LogNormal(1d, 2d);
Assert.AreEqual("LogNormal(μ = 1, σ = 2)", n.ToString());
}
public void ValidateMode(double mu, double sigma, double mode)
{
var n = new LogNormal(mu, sigma);
Assert.AreEqual(mode, n.Mode);
}
public void CanSampleSequence()
{
var n = new LogNormal(1.0, 2.0);
var ied = n.Samples();
ied.Take(5).ToArray();
}
public void ValidateDensity(double mu, double sigma, double x, double p)
{
var n = new LogNormal(mu, sigma);
AssertHelpers.AlmostEqual(p, n.Density(x), 14);
AssertHelpers.AlmostEqual(p, LogNormal.PDF(mu, sigma, x), 14);
}
public void SetSigmaFailsWithNegativeSigma()
{
var n = new LogNormal(1.0, 2.0);
Assert.Throws<ArgumentOutOfRangeException>(() => n.Sigma = -1.0);
}
public void CanSetMu(double mu)
{
var n = new LogNormal(1.0, 2.0);
n.Mu = mu;
}
public void ValidateToString()
{
var n = new LogNormal(1.0, 2.0);
AssertEx.AreEqual<string>("LogNormal(Mu = 1, Sigma = 2)", n.ToString());
}
public void SetSigmaFailsWithNegativeSigma()
{
var n = new LogNormal(1.0, 2.0);
n.Sigma = -1.0;
}
public void ValidateMedian(double mu, double sigma, double median)
{
var n = new LogNormal(mu, sigma);
Assert.AreEqual(median, n.Median);
}
public void ValidateMinimum()
{
var n = new LogNormal(1.0, 2.0);
Assert.AreEqual(0.0, n.Minimum);
}
public void SetSigmaFailsWithNegativeSigma()
{
var n = new LogNormal(1.0, 2.0);
Assert.That(() => n.Sigma = -1.0, Throws.ArgumentException);
}
public void ValidateSkewness(double mu, double sigma, double skewness)
{
var n = new LogNormal(mu, sigma);
AssertHelpers.AlmostEqualRelative(skewness, n.Skewness, 13);
}
public void ValidateCumulativeDistribution(double mu, double sigma, double x, double f)
{
var n = new LogNormal(mu, sigma);
AssertHelpers.AlmostEqualRelative(f, n.CumulativeDistribution(x), 7);
AssertHelpers.AlmostEqualRelative(f, LogNormal.CDF(mu, sigma, x), 7);
}
public void CanCreateLogNormal(double mu, double sigma)
{
var n = new LogNormal(mu, sigma);
Assert.AreEqual(mu, n.Mu);
Assert.AreEqual(sigma, n.Sigma);
}
public void ValidateDensityLn(double mu, double sigma, double x, double p)
{
var n = new LogNormal(mu, sigma);
AssertHelpers.AlmostEqualRelative(p, n.DensityLn(x), 13);
AssertHelpers.AlmostEqualRelative(p, LogNormal.PDFLn(mu, sigma, x), 13);
}
public void CanSample()
{
var n = new LogNormal(1.0, 2.0);
n.Sample();
}
public void ValidateEntropy(double mu, double sigma, double entropy)
{
var n = new LogNormal(mu, sigma);
AssertHelpers.AlmostEqualRelative(entropy, n.Entropy, 14);
}
public void ValidateInverseCumulativeDistribution(double mu, double sigma, double x, double f)
{
var n = new LogNormal(mu, sigma);
AssertHelpers.AlmostEqualRelative(x, n.InverseCumulativeDistribution(f), 8);
AssertHelpers.AlmostEqualRelative(x, LogNormal.InvCDF(mu, sigma, f), 8);
}
public void CanSetSigma(double sigma)
{
var n = new LogNormal(1.0, 2.0);
n.Sigma = sigma;
}