/// <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 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);
}