Continuous Distributions in C# QuickStart Sample

Illustrates how to use the classes that represent continuous probability distributions in the Extreme.Statistics.Distributions namespace in C#.

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using System;

using Extreme.Mathematics.Random;
using Extreme.Statistics;
using Extreme.Statistics.Distributions;

namespace Extreme.Numerics.Quickstart.CSharp
    /// <summary>
    /// Demonstrates how to use classes that implement
    /// continuous probabililty distributions.
    /// </summary>
    class ContinuousDistributions
        static void Main(string[] args)
            // The license is verified at runtime. We're using
            // a demo license here. For more information, see
            Extreme.License.Verify("Demo license");

            // This QuickStart Sample demonstrates the capabilities of
            // the classes that implement continuous probability distributions.
            // These classes inherit from the ContinuousDistribution class.
            // For an illustration of classes that implement discrete probability
            // distributions, see the DiscreteDistributions QuickStart Sample.
            // We illustrate the properties and methods of continuous distribution
            // using a Weibull distribution. The same properties and methods
            // apply to all other continuous distributions.

            // Constructing distributions

            // Most distributions have one or more parameters with different definitions.
            // The location parameter is always related to the mean of the distribution.
            // When omitted, its default value is zero.
            // The scale parameter is always directly related to the standard deviation.
            // A larger scale parameter means that the distribution is wider.
            // When omitted, its default value is one.

            // The Weibull distribution has three constructors. The most complete
            // constructor takes a location, scale, and shape parameter.
            WeibullDistribution weibull = new WeibullDistribution(3, 2, 3);

            // Basic statistics

            // The Mean property returns the mean of the distribution:
            Console.WriteLine("Mean:                 {0:F5}", weibull.Mean);

            // The Variance and StandardDeviation are also available:
            Console.WriteLine("Variance:             {0:F5}", weibull.Variance);
            Console.WriteLine("Standard deviation:   {0:F5}", weibull.StandardDeviation);
            // The inter-quartile range is another measure of scale:
            Console.WriteLine("Inter-quartile range: {0:F5}", weibull.InterQuartileRange);

            // As are the skewness:
            Console.WriteLine("Skewness:             {0:F5}", weibull.Skewness);

            // The Kurtosis property returns the kurtosis supplement.
            // The Kurtosis property for the normal distribution returns zero.
            Console.WriteLine("Kurtosis:             {0:F5}", weibull.Kurtosis);

            // Distribution functions

            // The (cumulative) distribution function (CDF) is implemented by the
            // DistributionFunction method:
            Console.WriteLine("CDF(4.5) =            {0:F5}", weibull.DistributionFunction(4.5));

            // Its complement is the survivor function:
            Console.WriteLine("SDF(4.5) =            {0:F5}", weibull.SurvivorDistributionFunction(4.5));

            // While its inverse is given by the InverseDistributionFunction method:
            Console.WriteLine("Inverse CDF(0.4) =    {0:F5}", weibull.InverseDistributionFunction(0.4));

            // The probability density function (PDF) is also available:
            Console.WriteLine("PDF(4.5) =            {0:F5}", weibull.ProbabilityDensityFunction(4.5));
            // The Probability method returns the probability that a variate lies between two values:
            Console.WriteLine("Probability(4.5, 5.5) = {0:F5}", weibull.Probability(4.5, 5.5));

            // Random variates

            // The Sample method returns a single random variate 
            // using the specified random number generator:
            System.Random rng = new MersenneTwister();
            double x = weibull.Sample(rng);
            // The SampleInto method fills an array or vector with
            // random variates. It has several overloads:
            double[] xArray = new double[100];
            // 1. Fill all values:
            weibull.SampleInto(rng, xArray);
            // 2. Fill only a range (start index and length are supplied)
            weibull.SampleInto(rng, xArray, 20, 50);
            // The same two options are available with a DenseVector
            // instead of a double array.

            // The GetExpectedHistogram method returns a Histogram that contains the
            // expected number of samples in each bin, given the total number of samples.
            // The bins are specified by lower and upper bounds and number of bins:
            var h = weibull.GetExpectedHistogram(3.0, 10.0, 5, 100);
            Console.WriteLine("Expected distribution of 100 samples:");

            // or by supplying an array of boundaries:
            h = weibull.GetExpectedHistogram(new double[] {3.0, 5.2, 7.4, 9.6, 11.8}, 100);
            Console.WriteLine("Expected distribution of 100 samples:");

            Console.Write("Press any key to exit.");