Extreme Optimization™: Complexity made simple.

Math and Statistics
Libraries for .NET

  • Home
  • Features
    • Math Library
    • Vector and Matrix Library
    • Statistics Library
    • Performance
    • Usability
  • Documentation
    • Introduction
    • Math Library User's Guide
    • Vector and Matrix Library User's Guide
    • Data Analysis Library User's Guide
    • Statistics Library User's Guide
    • Reference
  • Resources
    • Downloads
    • QuickStart Samples
    • Sample Applications
    • Frequently Asked Questions
    • Technical Support
  • Blog
  • Order
  • Company
    • About us
    • Testimonials
    • Customers
    • Press Releases
    • Careers
    • Partners
    • Contact us
Introduction
Deployment Guide
Configuration
Using Parallelism
Expand Mathematics Library User's GuideMathematics Library User's Guide
Expand Vector and Matrix Library User's GuideVector and Matrix Library User's Guide
Expand Data Analysis Library User's GuideData Analysis Library User's Guide
Expand Statistics Library User's GuideStatistics Library User's Guide
Expand Data Access Library User's GuideData Access Library User's Guide
Expand ReferenceReference
  • Extreme Optimization
    • Features
    • Solutions
    • Documentation
    • QuickStart Samples
    • Sample Applications
    • Downloads
    • Technical Support
    • Download trial
    • How to buy
    • Blog
    • Company
    • Resources
  • Documentation
    • Introduction
    • Deployment Guide
    • Configuration
    • Using Parallelism
    • Mathematics Library User's Guide
    • Vector and Matrix Library User's Guide
    • Data Analysis Library User's Guide
    • Statistics Library User's Guide
    • Data Access Library User's Guide
    • Reference
  • Reference
    • Extreme
    • Extreme.Collections
    • Extreme.Data
    • Extreme.Data.Json
    • Extreme.Data.Matlab
    • Extreme.Data.R
    • Extreme.Data.Stata
    • Extreme.Data.Text
    • Extreme.DataAnalysis
    • Extreme.DataAnalysis.Linq
    • Extreme.Mathematics
    • Extreme.Mathematics.Algorithms
    • Extreme.Mathematics.Calculus
    • Extreme.Mathematics.Calculus.OrdinaryDifferentialEquations
    • Extreme.Mathematics.Curves
    • Extreme.Mathematics.Curves.Nonlinear
    • Extreme.Mathematics.Distributed
    • Extreme.Mathematics.Distributed.Cuda
    • Extreme.Mathematics.EquationSolvers
    • Extreme.Mathematics.FSharp
    • Extreme.Mathematics.Generic
    • Extreme.Mathematics.Generic.LinearAlgebra
    • Extreme.Mathematics.Generic.LinearAlgebra.Implementation
    • Extreme.Mathematics.Generic.LinearAlgebra.Providers
    • Extreme.Mathematics.Generic.SignalProcessing
    • Extreme.Mathematics.Implementation
    • Extreme.Mathematics.LinearAlgebra
    • Extreme.Mathematics.LinearAlgebra.Complex
    • Extreme.Mathematics.LinearAlgebra.Complex.Decompositions
    • Extreme.Mathematics.LinearAlgebra.Implementation
    • Extreme.Mathematics.LinearAlgebra.IO
    • Extreme.Mathematics.LinearAlgebra.IterativeSolvers
    • Extreme.Mathematics.LinearAlgebra.IterativeSolvers.Preconditioners
    • Extreme.Mathematics.LinearAlgebra.Providers
    • Extreme.Mathematics.LinearAlgebra.Sparse
    • Extreme.Mathematics.Optimization
    • Extreme.Mathematics.Optimization.Genetic
    • Extreme.Mathematics.Optimization.LineSearches
    • Extreme.Mathematics.Random
    • Extreme.Mathematics.SignalProcessing
    • Extreme.Numerics.FSharp
    • Extreme.Statistics
    • Extreme.Statistics.Distributions
    • Extreme.Statistics.IO
    • Extreme.Statistics.Linq
    • Extreme.Statistics.Multivariate
    • Extreme.Statistics.Random
    • Extreme.Statistics.Tests
    • Extreme.Statistics.TimeSeriesAnalysis
  • Extreme.Statistics.Distributions
    • BernoulliDistribution Class
    • BetaDistribution Class
    • BinomialDistribution Class
    • CauchyDistribution Class
    • ChiSquareDistribution Class
    • ContinuousDistribution Class
    • ContinuousUniformDistribution Class
    • DirichletDistribution Class
    • DiscreteDistribution Class
    • DiscreteUniformDistribution Class
    • Distribution Class
    • ErlangDistribution Class
    • EstimationMethod Enumeration
    • ExponentialDistribution Class
    • FDistribution Class
    • GammaDistribution Class
    • GaussianMixtureDistribution Class
    • GeneralizedParetoDistribution Class
    • GenericDiscreteDistribution Class
    • GeometricDistribution Class
    • GumbelDistribution Class
    • HyperbolicDistribution Class
    • HypergeometricDistribution Class
    • InverseChiSquareDistribution Class
    • InverseGammaDistribution Class
    • InverseGaussianDistribution Class
    • InverseWeibullDistribution Class
    • LaplaceDistribution Class
    • LogarithmicSeriesDistribution Class
    • LogisticDistribution Class
    • LogLogisticDistribution Class
    • LognormalDistribution Class
    • MaxwellDistribution Class
    • MultivariateContinuousDistribution Class
    • MultivariateNormalDistribution Class
    • NegativeBinomialDistribution Class
    • NonCentralBetaDistribution Class
    • NonCentralChiSquareDistribution Class
    • NonCentralFDistribution Class
    • NonCentralStudentTDistribution Class
    • NormalDistribution Class
    • NormalInverseGaussianDistribution Class
    • ParetoDistribution Class
    • ParetoDistributionVariant Enumeration
    • PiecewiseDistribution Class
    • PoissonDistribution Class
    • RandomExtensions Class
    • RayleighDistribution Class
    • StudentTDistribution Class
    • TransformedBetaDistribution Class
    • TransformedGammaDistribution Class
    • TriangularDistribution Class
    • TruncatedDistribution Class
    • WeibullDistribution Class
    • WishartDistribution Class
  • BinomialDistribution Class
    • BinomialDistribution Constructors
    • Properties
    • Methods
BinomialDistribution ClassExtreme Optimization Numerical Libraries for .NET Professional
Represents the binomial distribution.
Inheritance Hierarchy

SystemObject
  Extreme.Statistics.DistributionsDistribution
    Extreme.Statistics.DistributionsDiscreteDistribution
      Extreme.Statistics.DistributionsBinomialDistribution

Namespace: Extreme.Statistics.Distributions
Assembly: Extreme.Numerics.Net40 (in Extreme.Numerics.Net40.dll) Version: 6.0.16073.0 (6.0.16312.0)
Syntax

C#
VB
C++
F#
Copy
[SerializableAttribute]
public class BinomialDistribution : DiscreteDistribution
<SerializableAttribute>
Public Class BinomialDistribution
	Inherits DiscreteDistribution
[SerializableAttribute]
public ref class BinomialDistribution : public DiscreteDistribution
[<SerializableAttribute>]
type BinomialDistribution =  
    class
        inherit DiscreteDistribution
    end

The BinomialDistribution type exposes the following members.

Constructors

  NameDescription
Public methodBinomialDistribution(Int32)
Constructs a new BinomialDistribution with the specified number of trials. The probability of success is set to 0.5.
Public methodBinomialDistribution(NumericalVariable)
Estimates the parameters of the distribution of a variable assuming it follows a binomial distribution.
Public methodBinomialDistribution(VectorDouble)
Estimates the parameters of the distribution of a variable assuming it follows a binomial distribution.
Public methodBinomialDistribution(Int32, VectorDouble)
Estimates the parameters of the distribution of a variable assuming it follows a binomial distribution.
Public methodBinomialDistribution(Int32, Double)
Constructs a new BinomialDistribution with the specified number of trials and probability of success.
Public methodBinomialDistribution(Int32, NumericalVariable)
Estimates the parameters of the distribution of a variable assuming it follows a binomial distribution.
Top
Properties

  NameDescription
Public propertyKurtosis
Gets the kurtosis of the distribution.
(Overrides DistributionKurtosis.)
Public propertyMean
Gets the mean or expectation value of the distribution.
(Overrides DistributionMean.)
Public propertyNumberOfTrials
Gets the number of trials.
Public propertyProbabilityOfSuccess
Gets the probability that a trial is successful.
Public propertySkewness
Gets the skewness of the distribution.
(Overrides DistributionSkewness.)
Public propertyStandardDeviation
Gets the standard deviation of the distribution.
(Inherited from Distribution.)
Public propertyStatisticSymbol
Gets the common symbol to describe a statistic from the distribution.
(Inherited from Distribution.)
Public propertyVariance
Gets the variance of the distribution.
(Overrides DistributionVariance.)
Top
Methods

  NameDescription
Public methodDistributionFunction
Evaluates the cumulative distribution function of the distribution.
(Overrides DiscreteDistributionDistributionFunction(Int32).)
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetExpectedHistogram(Double)
Gets a vector whose bins contain the expected number of samples for a given total number of samples.
Public methodGetExpectedHistogram(IndexIntervalInt32, Double)
Returns a histogram whose bins contain the expected number of samples from the distribution for a given total number of samples.
(Inherited from DiscreteDistribution.)
Public methodGetExpectedHistogram(IndexInt32, Double)
Returns a histogram whose bins contain the expected number of samples from the distribution for a given total number of samples.
(Inherited from DiscreteDistribution.)
Public methodGetExpectedHistogram(Int32, Int32, Double)
Returns a histogram whose bins contain the expected number of samples from the distribution for a given total number of samples.
(Inherited from DiscreteDistribution.)
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetRandomSequence
Returns a sequence of random samples from the distribution.
(Inherited from DiscreteDistribution.)
Public methodGetRandomSequence(Random)
Returns a sequence of random samples from the distribution.
(Inherited from DiscreteDistribution.)
Public methodGetRandomSequence(Random, Int32)
Returns a sequence of random samples of the specified length from the distribution.
(Inherited from DiscreteDistribution.)
Public methodGetRandomVariate(Random)
Returns a random sample from the distribution.
(Inherited from DiscreteDistribution.)
Public methodStatic memberGetRandomVariate(Random, Int32)
Returns a single random sample from a binomial distribution with the specified parameters. The probability of a trial resulting in a success is set to 0.5.
Public methodStatic memberGetRandomVariate(Random, Int32, Double) Obsolete.
Returns a single random sample from a binomial distribution with the specified parameters.
Public methodGetRandomVariates(Random, Int32)
Fills an Int32 array with random numbers.
(Inherited from DiscreteDistribution.)
Public methodGetRandomVariates(Random, Int32, Int32, Int32)
Fills an Int32 array with random numbers from this DiscreteDistribution.
(Inherited from DiscreteDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInverseDistributionFunction
Returns the inverse of the distribution function.
(Overrides DiscreteDistributionInverseDistributionFunction(Double).)
Public methodLeftTailProbability
Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound.
(Inherited from DiscreteDistribution.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbability(Int32)
Evaluates the probability function of the distribution.
(Overrides DiscreteDistributionProbability(Int32).)
Public methodProbability(Int32, Int32)
Gets the probability of obtaining a sample that falls within the specified interval from the distribution.
(Inherited from DiscreteDistribution.)
Public methodRightTailProbability
Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound.
(Inherited from DiscreteDistribution.)
Public methodSample
Returns a random sample from the distribution.
(Inherited from DiscreteDistribution.)
Public methodSample(Random)
Returns a random sample from the distribution.
(Overrides DiscreteDistributionSample(Random).)
Public methodSample(Int32)
Returns a vector of random samples from the distribution.
(Inherited from DiscreteDistribution.)
Public methodStatic memberSample(Random, Int32)
Returns a single random sample from a binomial distribution with the specified parameters. The probability of a trial resulting in a success is set to 0.5.
Public methodSample(Int32, Random)
Returns a vector of random samples from the distribution.
(Inherited from DiscreteDistribution.)
Public methodSample(Random, Int32)
Fills an Int32 array with random numbers.
(Inherited from DiscreteDistribution.)
Public methodStatic memberSample(Random, Int32, Double)
Returns a single random sample from a binomial distribution with the specified parameters.
Public methodSample(Random, Int32, Int32, Int32)
Fills an Int32 array with random numbers from this DiscreteDistribution.
(Inherited from DiscreteDistribution.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Public methodToString
Returns a string that represents the current object.
(Overrides ObjectToString.)
Public methodTwoTailProbability
Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound.
(Inherited from DiscreteDistribution.)
Top
Remarks

The binomial distribution Binomial(n, probability) characterizes the probability of the number of successes in a variable of n trials, each having a probability probability of being successful.

If n = 1, the binomial distribution reduces to the BernoulliDistribution.

Examples

The number of dice showing a six when rolling N dice has a biomial distribution with n = N and probability = 1/6. Notice that it doesn't matter if the trials are run simultaneously or in succession.
Version Information

Numerical Libraries

Supported in: 6.0, 5.x, 4.x
See Also

Reference

Extreme.Statistics.Distributions Namespace
Extreme.Statistics.DistributionsBernoulliDistribution
Extreme.Statistics.DistributionsGeometricDistribution
Extreme.Statistics.DistributionsNegativeBinomialDistribution

Copyright (c) 2004-2016 ExoAnalytics Inc.

Send comments on this topic to support@extremeoptimization.com

Copyright © 2004-2018, Extreme Optimization. All rights reserved.
Extreme Optimization, Complexity made simple, M#, and M Sharp are trademarks of ExoAnalytics Inc.
Microsoft, Visual C#, Visual Basic, Visual Studio, Visual Studio.NET, and the Optimized for Visual Studio logo
are registered trademarks of Microsoft Corporation.