Data Analysis Mathematics Linear Algebra Statistics
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QuickStart Samples

# Discrete Distributions QuickStart Sample (Visual Basic)

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

```Option Infer On

Imports Extreme.DataAnalysis
Imports Extreme.Mathematics.Random
Imports Extreme.Statistics.Distributions

Namespace Extreme.Numerics.QuickStart.VB
' Demonstrates how to use classes that implement
' discrete probabililty distributions.
Module DiscreteDistributions

Sub Main()
' 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:
Dim binomial As 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:
Dim rng As New MersenneTwister
Dim x As Integer = binomial.Sample(rng)
' The Sample method fills an array or vector with
' random variates. It has several overloads:
Dim xArray As Integer() = New Integer(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:
Dim h = binomial.GetExpectedHistogram(100)
Console.WriteLine("Expected distribution of 100 samples:")
For i = 0 To h.Length - 1
Console.WriteLine("{0} success(es) -> {1}", i, h(i))
Next
Console.WriteLine()

Console.WriteLine("Press Enter key to continue.")