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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: 4.1.4
public sealed class BetaDistribution : ContinuousDistribution

The BetaDistribution type exposes the following members.

Public methodBetaDistribution
Initializes a new β distribution.
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 ContinuousDistribution.)
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 non-vanishing.
(Overrides ContinuousDistributionSupport.)
Public propertyVariance
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.)
Public methodCentralMoment
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)
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 ContinuousDistribution.)
Public methodStatic memberFitToSample
Computes the Beta distribution that best fits the given sample.
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetRandomValue
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).)
Public methodGetRandomValues
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodHazard
Computes the hazard function.
(Inherited from ContinuousDistribution.)
Public methodInverseLeftProbability
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).)
Public methodInverseRightProbability
Returns the point at which the right probability function attains the given value.
(Overrides ContinuousDistributionInverseRightProbability(Double).)
Public methodLeftProbability
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)
Public methodProbabilityDensity
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)
Public methodRawMoment
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)
Public methodRightProbability
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)

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

The left shape parameter α controls the shape of the distribution near the left endpoint x = 0. The right shapre paramater β controls the shape of the distribution near the right endpoint x = 1. If a shape parameter is less than one, the distribution is singular on that side. If a shape parameter is greater than one, the distribution does to zero on that side. If a shape parameter is equal to one, the distribution goes to a constant on that side.

If the two shape parameters are equal, the distribution is symmetric.

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).

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

In fact, the ith order statistic (ith smallest value) in n draws from a uniform distribution is distributed as B(i, n - i + 1).

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

See Also