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Extreme Optimization QuickStart Samples

Continuous Distributions QuickStart Sample (F#)

Illustrates how to use the classes that implement continuous probability distributions (Extreme.Statistics.Distributions namespace) in F#.

C# code VB.NET code Back to QuickStart Samples

#light
 
open System
 
open Extreme.Statistics
open Extreme.Statistics.Distributions
 
/// <summary>
/// Demonstrates how to use classes that implement
/// continuous probabililty distributions.
/// </summary>
 
// 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.
let weibull = new WeibullDistribution(3.0, 2.0, 3.0)
 
//
// 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)
Console.WriteLine()
 
//
// 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))
Console.WriteLine()
 
//
// Random variates
//
 
// The GetRandomVariate method returns a single random variate 
// using the specified random number generator:
let rng = new Random.MersenneTwister()
let x = weibull.GetRandomVariate(rng)
// The GetRandomVariates method fills an array or vector with
// random variates. It has several overloads:
open Microsoft.FSharp.Collections.Array
let xArray = (Array.create 100) 1.0
// 1. Fill all values:
weibull.GetRandomVariates(rng, xArray)
// 2. Fill only a range (start index and length are supplied)
weibull.GetRandomVariates(rng, xArray, 20, 50)
// The same two options are available with a GeneralVector
// instead of a double array.
 
let printBins (h : Histogram) =
   for bin in h.Bins do 
      Console.WriteLine("Between {0} and {1} -> {2}", bin.LowerBound, bin.UpperBound, bin.Value)
   done
 
// 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:
let h = weibull.GetExpectedHistogram(3.0, 10.0, 5, 100.0)
Console.WriteLine("Expected distribution of 100 samples:")
printBins h
 
// or by supplying an array of boundaries:
h = weibull.GetExpectedHistogram([|3.0; 5.2; 7.4; 9.6; 11.8|], 100.0)
Console.WriteLine("Expected distribution of 100 samples:")
printBins h
 
Console.Write("Press any key to exit.")
Console.ReadLine()

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