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BetaDistribution Class
Represents a beta distribution.
Inheritance Hierarchy

Namespace:  Meta.Numerics.Statistics.Distributions
Assembly:  Meta.Numerics (in Meta.Numerics.dll) Version: 3.1.0.0 (3.1.0.0)
Syntax
public sealed class BetaDistribution : Distribution

The BetaDistribution type exposes the following members.

Constructors
  NameDescription
Public methodBetaDistribution
Initializes a new β distribution.
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Properties
  NameDescription
Public propertyAlpha
Gets the left shape parameter.
Public propertyBeta
Gets the right shape parameter.
Public propertyExcessKurtosis
Gets the excess kurtosis of the distribution.
(Inherited from UnivariateDistribution.)
Public propertyMean
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)
Public propertyMedian
Gets the median of the distribution.
(Inherited from Distribution.)
Public propertySkewness
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)
Public propertyStandardDeviation
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)
Public propertySupport
Gets the interval over which the distribution is nonvanishing.
(Overrides DistributionSupport.)
Public propertyVariance
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.)
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Methods
  NameDescription
Public methodCumulant
Computes a cumulant of the distribution.
(Inherited from UnivariateDistribution.)
Public methodEquals
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
Public methodExpectationValue
Computes the expectation value of the given function.
(Inherited from Distribution.)
Public methodStatic memberFitToSample
Computes the Beta distribution that best fits the given sample.
Public methodGetHashCode
Serves as a hash function for a particular type.
(Inherited from Object.)
Public methodGetRandomValue
Returns a random value.
(Overrides DistributionGetRandomValue(Random).)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInverseLeftProbability
Returns the point at which the cumulative distribution function attains a given value.
(Overrides DistributionInverseLeftProbability(Double).)
Public methodInverseRightProbability
Returns the point at which the right probability function attains the given value.
(Overrides DistributionInverseRightProbability(Double).)
Public methodLeftProbability
Returns the cumulative probability to the left of (below) the given point.
(Overrides DistributionLeftProbability(Double).)
Public methodMoment
Computes a raw moment of the distribution.
(Overrides DistributionMoment(Int32).)
Public methodMomentAboutMean
Computes a central moment of the distribution.
(Overrides DistributionMomentAboutMean(Int32).)
Public methodProbabilityDensity
Returns the probability density at the given point.
(Overrides DistributionProbabilityDensity(Double).)
Public methodRightProbability
Return the cumulative probability to the right of (above) the given point.
(Overrides DistributionRightProbability(Double).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Remarks

The beta distribution is defined on the interval [0,1]. Depending on its two shape parameters, it can take on a wide variety of forms on this interval.

If the two shape parameters are equal, the distribution is symmetric. If the first shape parameter is less than one, the distribution has a singularity at its left endpoint. If the first shape parameter is greater than one, the distribution goes to zero at its left endpoint. The second shape parameter similarly governs the distribution's behavior at its right endpoint.

When both shape parameters are one, the beta distribution reduces to a standard uniform distribution.

Beta distributions describe the maximum and minimum values obtained from multiple, independent draws from a standard uniform distribution. For n draws, the maximum value is distributed as B(n,1).

Similiarly, the minimum value is distributed as B(1,n).

Because of the wide variety of shapes it can take, the beta distribution is sometimes used as an ad hoc model to describe any distribution observed on a finite interval.

See Also