BetaDistribution Class

Represents the Beta distribution.

Definition

Namespace: Numerics.NET.Statistics.Distributions
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4
C#
[SerializableAttribute]
public class BetaDistribution : ContinuousDistribution
Inheritance
Object  →  Distribution  →  ContinuousDistribution  →  BetaDistribution
Derived

Remarks

Beta distributions have two shape parameters, usually called α and β.

Unlike most other distributions, location and scale parameters are not usually used to specify the general form of the Beta distribution. Instead, the lower and upper bounds of the definition interval are used. This interval defaults to [0, 1].

A beta distribution with both shape parameters equal to 1 reduces to a Uniform distribution. If α=1 and β = 2, or α = 2 and β = 1, the beta distribution reduces to the triangular distribution.

Constructors

BetaDistribution(Vector<Double>) Constructs the beta distribution from a numerical variable.
BetaDistribution(Double, Double) Constructs a new BetaDistribution using the specified shape parameters.
BetaDistribution(Vector<Double>, EstimationMethod) Constructs the beta distribution from a numerical variable.
BetaDistribution(Double, Double, Double, Double) Constructs a new BetaDistribution using the specified shape parameters.

Properties

Alpha Gets the first shape parameter of this BetaDistribution.
Beta Gets the first shape parameter of this BetaDistribution.
Capabilities Gets a value that indicates the capabilities of the distribution class.
(Inherited from Distribution)
Entropy Gets the entropy of the distribution.
(Overrides Distribution.Entropy)
InterQuartileRange Returns the inter-quartile range of this distribution.
(Inherited from ContinuousDistribution)
IsSymmetrical Gets whether the distribution is known to be symmetrical around the mean.
(Overrides ContinuousDistribution.IsSymmetrical)
IsUnimodal Gets whether the distribution has one or more modes.
(Inherited from ContinuousDistribution)
Kurtosis Gets the kurtosis of the distribution.
(Overrides Distribution.Kurtosis)
LowerBound Gets the lower bound of the interval on which this BetaDistribution is defined.
Mean Gets the mean or expectation value of the distribution.
(Overrides Distribution.Mean)
Median Gets the median of the distribution.
(Inherited from ContinuousDistribution)
Mode Gets the mode of the distribution.
(Overrides ContinuousDistribution.Mode)
NumberOfModes Gets the number of modes of the distribution.
(Overrides ContinuousDistribution.NumberOfModes)
Skewness Gets the skewness of the distribution.
(Overrides Distribution.Skewness)
StandardDeviation Gets the standard deviation of the distribution.
(Inherited from Distribution)
StatisticSymbol Gets the common symbol to describe a statistic from the distribution.
(Inherited from Distribution)
Support Gets the support of the distribution.
(Overrides ContinuousDistribution.Support)
UpperBound Gets the upper bound of the interval on which this BetaDistribution is defined.
Variance Gets the variance of the distribution.
(Overrides Distribution.Variance)

Methods

Cdf Evaluates the cumulative distribution function (CDF) of this distribution for the specified value.
(Inherited from ContinuousDistribution)
DistributionFunction Evaluates the cumulative distribution function (CDF) of this distribution for the specified value.
(Overrides ContinuousDistribution.DistributionFunction(Double))
EqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
FinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
GetAllModes Returns an array that contains all the modes of the distribution.
(Overrides ContinuousDistribution.GetAllModes())
GetExpectationValue(Func<Double, Double>) Returns the expectation value of a function.
(Inherited from ContinuousDistribution)
GetExpectationValue(Func<Double, Double>, Double, Double) Returns the un-normalized expectation value of a function over the specified interval.
(Inherited from ContinuousDistribution)
GetExpectedHistogram(Double[], Double) Gets a vector containing a histogram of the expected number of samples for a given total number of samples.
(Inherited from ContinuousDistribution)
GetExpectedHistogram(IntervalIndex<Double>, Double) Gets a vector containing a histogram of the expected number of samples for a given total number of samples.
(Inherited from ContinuousDistribution)
GetExpectedHistogram(Double, Double, Int32, Double) Gets a vector whose bins contain the expected number of samples for a given total number of samples.
(Inherited from ContinuousDistribution)
GetHashCodeServes as the default hash function.
(Inherited from Object)
GetRandomSequence() Returns a sequence of random samples from the distribution.
(Inherited from ContinuousDistribution)
GetRandomSequence(Random) Returns a sequence of random samples from the distribution.
(Inherited from ContinuousDistribution)
GetRandomSequence(Random, Int32) Returns a sequence of random samples of the specified length from the distribution.
(Inherited from ContinuousDistribution)
GetTypeGets the Type of the current instance.
(Inherited from Object)
HazardFunction Returns the probability of failure at the specified value.
(Inherited from ContinuousDistribution)
InverseCdf Returns the inverse of the DistributionFunction(Double).
(Inherited from ContinuousDistribution)
InverseDistributionFunction Returns the inverse of the DistributionFunction(Double).
(Overrides ContinuousDistribution.InverseDistributionFunction(Double))
LeftTailProbability Returns the probability that a sample from the distribution is less than the specified value.
(Inherited from ContinuousDistribution)
LogProbabilityDensityFunction Returns the logarithm of the probability density function (PDF) of this distribution for the specified value.
(Overrides ContinuousDistribution.LogProbabilityDensityFunction(Double))
MemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
MomentFunction Returns the value of the moment function of the specified order.
(Overrides ContinuousDistribution.MomentFunction(Int32, Double))
Pdf Returns the value of the probability density function (PDF) of this distribution for the specified value.
(Inherited from ContinuousDistribution)
Probability Returns the probability that a sample taken from the distribution lies inside the specified interval.
(Inherited from ContinuousDistribution)
ProbabilityDensityFunction Returns the value of the probability density function (PDF) of this distribution for the specified value.
(Overrides ContinuousDistribution.ProbabilityDensityFunction(Double))
RightTailProbability Returns the probability that a sample from the distribution is larger than the specified value.
(Inherited from ContinuousDistribution)
Sample() Returns a random sample from the distribution.
(Inherited from ContinuousDistribution)
Sample(Int32) Returns a vector of random samples from the distribution.
(Inherited from ContinuousDistribution)
Sample(Random) Returns a random sample from the distribution.
(Overrides ContinuousDistribution.Sample(Random))
Sample(Int32, Random) Returns a vector of random samples from the distribution.
(Inherited from ContinuousDistribution)
Sample(Random, Double, Double) Returns a single random sample from a beta distribution with the specified parameters.
SampleInto(Random, IList<Double>) Fills a list with random numbers from the distribution.
(Inherited from ContinuousDistribution)
SampleInto(Random, Double[]) Fills a list with random numbers from the distribution.
(Inherited from ContinuousDistribution)
SampleInto(Random, Span<Double>) Fills a span with random numbers from the distribution.
(Inherited from ContinuousDistribution)
SampleInto(Random, IList<Double>, Int32, Int32) Fills part of a list with random numbers from the distribution.
(Inherited from ContinuousDistribution)
SurvivorDistributionFunction Evaluates the survivor distribution function (SDF) of this distribution for the specified value.
(Inherited from ContinuousDistribution)
ToStringReturns a string that represents the current object.
(Overrides Object.ToString())
TwoTailedProbability Returns the probability that a sample from the distribution deviates from the mean more than the specified value.
(Inherited from ContinuousDistribution)

See Also