BetaDistribution Class

public sealed class BetaDistribution : ContinuousDistribution

Public NotInheritable Class BetaDistribution
	Inherits ContinuousDistribution

public ref class BetaDistribution sealed : public ContinuousDistribution

[<SealedAttribute>]
type BetaDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance

Object    UnivariateDistribution    ContinuousDistribution    BetaDistribution

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 goes 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.

Reference

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