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• BinomialDistribution Class
  • BinomialDistribution Constructors
  • Properties
  • Methods

BinomialDistribution Class

Extreme 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 (in Extreme.Numerics.dll) Version: 8.1.1

Syntax

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C#

VB

C++

F#

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[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

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

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Properties

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	Name	Description
	Entropy	Gets the entropy of the distribution. (Overrides DistributionEntropy.)
	IsUnimodal	Gets whether the distribution has one or more modes. (Inherited from DiscreteDistribution.)
	Kurtosis	Gets the kurtosis of the distribution. (Overrides DistributionKurtosis.)
	Mean	Gets the mean or expectation value of the distribution. (Overrides DistributionMean.)
	Mode	Gets the mode of the distribution. (Overrides DiscreteDistributionMode.)
	NumberOfModes	Gets the number of modes of the distribution. (Overrides DiscreteDistributionNumberOfModes.)
	NumberOfTrials	Gets the number of trials.
	ProbabilityOfSuccess	Gets the probability that a trial is successful.
	Skewness	Gets the skewness of the distribution. (Overrides DistributionSkewness.)
	StandardDeviation	Gets the standard deviation of the distribution. (Inherited from Distribution.)
	StatisticSymbol	Gets the common symbol to describe a statistic from the distribution. (Inherited from Distribution.)
	Variance	Gets the variance of the distribution. (Overrides DistributionVariance.)

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Methods

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	Name	Description
	DistributionFunction	Evaluates the cumulative distribution function of the distribution. (Overrides DiscreteDistributionDistributionFunction(Int32).)
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetAllModes	Returns an array that contains all the modes of the distribution. (Overrides DiscreteDistributionGetAllModes.)
	GetExpectedHistogram(Double)	Gets a vector whose bins contain the expected number of samples for a given total number of samples.
	GetExpectedHistogram(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.)
	GetExpectedHistogram(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.)
	GetExpectedHistogram(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.)
	GetHashCode	Serves as the default hash function. (Inherited from Object.)
	GetRandomSequence	Returns a sequence of random samples from the distribution. (Inherited from DiscreteDistribution.)
	GetRandomSequence(Random)	Returns a sequence of random samples from the distribution. (Inherited from DiscreteDistribution.)
	GetRandomSequence(Random, Int32)	Returns a sequence of random samples of the specified length from the distribution. (Inherited from DiscreteDistribution.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	InverseDistributionFunction	Returns the inverse of the distribution function. (Overrides DiscreteDistributionInverseDistributionFunction(Double).)
	LeftTailProbability	Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound. (Inherited from DiscreteDistribution.)
	LogProbability	Returns the logarithm of the probability of obtaining a specific integer value in the distribution. (Overrides DiscreteDistributionLogProbability(Int32).)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Probability(Int32)	Evaluates the probability function of the distribution. (Overrides DiscreteDistributionProbability(Int32).)
	Probability(Int32, Int32)	Gets the probability of obtaining a sample that falls within the specified interval from the distribution. (Inherited from DiscreteDistribution.)
	RightTailProbability	Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound. (Inherited from DiscreteDistribution.)
	Sample	Returns a random sample from the distribution. (Inherited from DiscreteDistribution.)
	Sample(Int32)	Returns a vector of random samples from the distribution. (Inherited from DiscreteDistribution.)
	Sample(Random)	Returns a random sample from the distribution. (Overrides DiscreteDistributionSample(Random).)
	Sample(Int32, Random)	Returns a vector of random samples from the distribution. (Inherited from DiscreteDistribution.)
	Sample(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.
	Sample(Random, Int32)	Fills an Int32 array with random numbers. (Inherited from DiscreteDistribution.)
	Sample(Random, Int32, Double)	Returns a single random sample from a binomial distribution with the specified parameters.
	Sample(Random, Int32, Int32, Int32)	Fills an Int32 array with random numbers from this DiscreteDistribution. (Inherited from DiscreteDistribution.)
	ToString	Returns a string that represents the current object. (Overrides ObjectToString.)
	TwoTailProbability	Gets the probability of obtaining a sample that is less than or less than or equal to the specified upper bound. (Inherited from DiscreteDistribution.)

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Remarks

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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

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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.

See Also

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Reference

Extreme.Statistics.Distributions Namespace

Extreme.Statistics.DistributionsBernoulliDistribution

Extreme.Statistics.DistributionsGeometricDistribution

Extreme.Statistics.DistributionsNegativeBinomialDistribution

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