Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 1.5.0.0 (1.5.0.0)
Syntax
| C# | Visual Basic | Visual C++ |
public class BetaDistribution : Distribution
Public Class BetaDistribution _ Inherits Distribution
public ref class BetaDistribution : public Distribution
Members
| All Members | Constructors  | Properties  | Methods |
 Public Protected | Instance Static  | Declared Inherited | XNA Framework Only  .NET Compact Framework Only  |
| Member | Description | |
|---|---|---|
| BetaDistribution(Double, Double) |
Instantiates a new β distribution.
|
| Alpha |
Gets the left shape parameter.
|
| Beta |
Gets the right shape parameter.
|
| Equals(Object) | (Inherited from Object.) |
| ExpectationValue(Function<(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.) |
| 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.
(Inherited from Distribution.) |
| 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.
(Inherited from Distribution.) |
| 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()()() | (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 second shape parameter is less than one, the distribution has a singularity 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 distributions on the unit interval it can describe, the beta distribution is sometimes used as an ad hoc model to describe any distribution observed on a finite interval.
Inheritance Hierarchy
Meta.Numerics.Statistics..::.Distribution
Meta.Numerics.Statistics..::.BetaDistribution
See Also
