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QuickStart Samples

Discrete Distributions QuickStart Sample (C#)

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

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using System;

using Extreme.Statistics;
using Extreme.Statistics.Distributions;

namespace Extreme.Statistics.Quickstart.CSharp
	/// <summary>
	/// Demonstrates how to use classes that implement
	/// discrete probabililty distributions.
	/// </summary>
	class DiscreteDistributions
		/// <summary>
		/// The main entry point for the application.
		/// </summary>
		static void Main(string[] args)
			// This QuickStart Sample demonstrates the capabilities of
			// the classes that implement discrete probability distributions.
			// These classes inherit from the DiscreteDistribution class.
			// For an illustration of classes that implement discrete probability
			// distributions, see the ContinuousDistributions QuickStart Sample.
			// We illustrate the properties and methods of discrete distribution
			// using a binomial distribution. The same properties and methods
			// apply to all other discrete distributions.

			// Constructing distributions

			// Many discrete probability distributions are related to Bernoulli trials,
			// events with a certain probability, p, of success. The number of trials
			// is often one of the distribution's parameters.

			// The binomial distribution has two constructors. Here, we create a
			// binomial distribution for 6 trials with a probability of success of 0.6:
			BinomialDistribution binomial = new BinomialDistribution(6, 0.6);

			// The distribution's parameters are available through the
			// NumberOfTrials and ProbabilityOfSuccess properties:
			Console.WriteLine("# of trials:          {0:F5}", binomial.NumberOfTrials);
			Console.WriteLine("Prob. of success:     {0:F5}", binomial.ProbabilityOfSuccess);

			// Basic statistics

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

			// The Variance and StandardDeviation are also available:
			Console.WriteLine("Variance:             {0:F5}", binomial.Variance);
			Console.WriteLine("Standard deviation:   {0:F5}", binomial.StandardDeviation);

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

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

			// Distribution functions

			// The (cumulative) distribution function (CDF) is implemented by the
			// DistributionFunction method:
			Console.WriteLine("CDF(4) =            {0:F5}", binomial.DistributionFunction(4));

			// The probability density function (PDF) is available as the 
			// Probability method:
			Console.WriteLine("PDF(4) =            {0:F5}", binomial.Probability(4));
			// The Probability method has an overload that returns the probability
			// that a variate lies between two values:
			Console.WriteLine("Probability(3, 5) = {0:F5}", binomial.Probability(3, 5));

			// Random variates

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

			// The GetExpectedHistogram method returns a Histogram that contains the
			// expected number of samples in each bin:
			Histogram h = binomial.GetExpectedHistogram(100);
			Console.WriteLine("Expected distribution of 100 samples:");
			foreach(HistogramBin bin in h.Bins)
				Console.WriteLine("{0} success(es) -> {1}", bin.LowerBound, bin.Value);

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