Represents a beta distribution.

Namespace: Meta.Numerics.Statistics.Distributions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 2.2.0.0 (2.2.0.0)

Syntax

            
 C#  Visual Basic  Visual C++  F# 
public sealed class BetaDistribution : Distribution
Public NotInheritable Class BetaDistribution
	Inherits Distribution
public ref class BetaDistribution sealed : public Distribution
[<SealedAttribute>]
type BetaDistribution =  
    class
        inherit Distribution
    end

Members

            
 All Members  Constructors   Properties   Methods  
 Public

 Protected
 Instance

 Static 
 Declared

 Inherited
 XNA Framework Only 

 .NET Compact Framework Only 

 MemberDescription
BetaDistribution(Double, Double)
Initializes a new β distribution.
Alpha
Gets the left shape parameter.
Beta
Gets the right shape parameter.
Equals(Object)
Determines whether the specified Object is equal to the current Object.
(Inherited from Object.)
ExpectationValue(Func<(Of <<'(Double, Double>)>>))
Computes the expectation value of the given function.
(Inherited from Distribution.)
Finalize()()()()
Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
(Inherited from Object.)
FitToSample(Sample)
Computes the Beta distribution that best fits the given sample.
GetHashCode()()()()
Serves as a hash function for a particular type.
(Inherited from Object.)
GetRandomValue(Random)
Returns a random value.
(Inherited from Distribution.)
GetType()()()()
Gets the Type of the current instance.
(Inherited from Object.)
InverseLeftProbability(Double)
Returns the point at which the cumulative distribution function attains a given value.
(Overrides Distribution..::..InverseLeftProbability(Double).)
InverseRightProbability(Double)
Returns the point at which the right probability function attains the given value.
(Overrides Distribution..::..InverseRightProbability(Double).)
LeftProbability(Double)
Returns the cumulative probability to the left of (below) the given point.
(Overrides Distribution..::..LeftProbability(Double).)
Mean
Gets the mean of the distribution.
(Overrides Distribution..::..Mean.)
Median
Gets the median of the distribution.
(Inherited from Distribution.)
MemberwiseClone()()()()
Creates a shallow copy of the current Object.
(Inherited from Object.)
Moment(Int32)
Returns the given moment of the distribution.
(Overrides Distribution..::..Moment(Int32).)
MomentAboutMean(Int32)
Returns the given moment of the distribution, about the mean.
(Overrides Distribution..::..MomentAboutMean(Int32).)
ProbabilityDensity(Double)
Returns the probability density at the given point.
(Overrides Distribution..::..ProbabilityDensity(Double).)
RightProbability(Double)
Return the cumulative probability to the right of (above) the given point.
(Overrides Distribution..::..RightProbability(Double).)
Skewness
Ges the skewness of the distribution.
(Overrides Distribution..::..Skewness.)
StandardDeviation
Gets the standard deviation of the distribution.
(Inherited from Distribution.)
Support
Gets the interval over which the distribution is nonvanishing.
(Overrides Distribution..::..Support.)
ToString()()()()
Returns a String that represents the current Object.
(Inherited from Object.)
Variance
Gets the variance of the distribution.
(Overrides Distribution..::..Variance.)

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.

Inheritance Hierarchy

System..::..Object
  Meta.Numerics.Statistics.Distributions..::..Distribution
    Meta.Numerics.Statistics.Distributions..::..BetaDistribution

See Also