BetaDistribution Class 
Namespace: Meta.Numerics.Statistics.Distributions
The BetaDistribution type exposes the following members.
Name  Description  

BetaDistribution 
Initializes a new β distribution.

Name  Description  

Alpha 
Gets the left shape parameter.
 
Beta 
Gets the right shape parameter.
 
ExcessKurtosis 
Gets the excess kurtosis of the distribution.
(Inherited from UnivariateDistribution.)  
Mean 
Gets the mean of the distribution.
(Overrides UnivariateDistributionMean.)  
Median 
Gets the median of the distribution.
(Inherited from ContinuousDistribution.)  
Skewness 
Gets the skewness of the distribution.
(Overrides UnivariateDistributionSkewness.)  
StandardDeviation 
Gets the standard deviation of the distribution.
(Inherited from UnivariateDistribution.)  
Support 
Gets the interval over which the distribution is nonvanishing.
(Overrides ContinuousDistributionSupport.)  
Variance 
Gets the variance of the distribution.
(Overrides UnivariateDistributionVariance.) 
Name  Description  

CentralMoment 
Computes a central moment of the distribution.
(Overrides ContinuousDistributionCentralMoment(Int32).)  
Cumulant 
Computes a cumulant of the distribution.
(Inherited from UnivariateDistribution.)  
Equals  Determines whether the specified object is equal to the current object. (Inherited from Object.)  
ExpectationValue 
Computes the expectation value of the given function.
(Inherited from ContinuousDistribution.)  
FitToSample 
Computes the Beta distribution that best fits the given sample.
 
GetHashCode  Serves as the default hash function. (Inherited from Object.)  
GetRandomValue 
Generates a random variate.
(Overrides ContinuousDistributionGetRandomValue(Random).)  
GetRandomValues 
Generates the given number of random variates.
(Inherited from ContinuousDistribution.)  
GetType  Gets the Type of the current instance. (Inherited from Object.)  
Hazard 
Computes the hazard function.
(Inherited from ContinuousDistribution.)  
InverseLeftProbability 
Returns the point at which the cumulative distribution function attains a given value.
(Overrides ContinuousDistributionInverseLeftProbability(Double).)  
InverseRightProbability 
Returns the point at which the right probability function attains the given value.
(Overrides ContinuousDistributionInverseRightProbability(Double).)  
LeftProbability 
Returns the cumulative probability to the left of (below) the given point.
(Overrides ContinuousDistributionLeftProbability(Double).)  
ProbabilityDensity 
Returns the probability density at the given point.
(Overrides ContinuousDistributionProbabilityDensity(Double).)  
RawMoment 
Computes a raw moment of the distribution.
(Overrides ContinuousDistributionRawMoment(Int32).)  
RightProbability 
Returns the cumulative probability to the right of (above) the given point.
(Overrides ContinuousDistributionRightProbability(Double).)  
ToString  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.