Discrete Distributions in C# QuickStart Sample
Illustrates how to use the classes that represent discrete probability distributions in the Extreme.Statistics.Distributions namespace in C#.
View this sample in: Visual Basic F# IronPython
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
/// discrete probabililty distributions.
/// </summary>
class DiscreteDistributions
{
static void Main(string[] args)
{
// The license is verified at runtime. We're using
// a demo license here. For more information, see
// https://numerics.net/trial-key
Extreme.License.Verify("Demo license");
// 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);
Console.WriteLine();
//
// 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));
Console.WriteLine();
//
// Random variates
//
// The Sample method returns a single random variate
// using the specified random number generator:
System.Random rng = new 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:
var h = binomial.GetExpectedHistogram(100);
Console.WriteLine("Expected distribution of 100 samples:");
Console.WriteLine(h.Summarize());
Console.WriteLine();
Console.Write("Press any key to exit.");
Console.ReadLine();
}
}
}