Represents the Beta distribution.
Namespace: Extreme.Statistics.Distributions
Assembly: Extreme.Numerics (Extreme.Numerics)
Syntax
| Visual Basic (Declaration) |
|---|
Public Class BetaDistribution _ Inherits ContinuousDistribution |
| C# |
|---|
public class BetaDistribution : ContinuousDistribution |
| C++ |
|---|
public ref class BetaDistribution : public ContinuousDistribution |
Methods
| Icon | Type | Description |
|---|---|---|
 | DistributionFunction(Double) |
Evaluates the cumulative distribution function
(CDF) of this distribution for the specified value.
|
| Equals(Object) | |
 | Finalize() | |
| GetExpectedHistogram(Double[](), Double) |
Gets a Histogram whose bins contain the expected number of samples
for a given total number of samples.
|
| GetExpectedHistogram(Double, Double, Int32, Double) |
Gets a Histogram whose bins contain the expected number of samples
for a given total number of samples.
|
| GetHashCode() | Serves as a hash function for a particular type. |
 | GetRandomVariate(Random, Double, Double) |
Returns a single random variate from a beta distribution
with the specified parameters.
|
| GetRandomVariate(Random) |
Returns a random sample from the distribution.
|
| GetRandomVariates(Random, Vector) |
Fills a Vector with random numbers.
|
| GetRandomVariates(Random, Double[]()) |
Fills a Double array with random numbers.
|
| GetRandomVariates(Random, Double[](), Int32, Int32) |
Fills a Double array with random numbers.
|
| GetRandomVariates(Random, Vector, Int32, Int32) |
Fills a Double array with random numbers.
|
| GetType() | Gets the Type of the current instance. |
| InverseDistributionFunction(Double) |
Returns the inverse of the DistributionFunction(Double).
|
| MemberwiseClone() | Creates a shallow copy of the current Object. |
| Probability(Double, Double) |
Returns the probability that a sample taken from the
distribution lies inside the specified interval.
|
| ProbabilityDensityFunction(Double) |
Returns the value of the probability density function
(PDF) of this distribution for the specified value.
|
| SurvivorDistributionFunction(Double) |
Evaluates the survivor distribution function
(SDF) of this distribution for the specified value.
|
| ToString() |
Constructors
| Icon | Type | Description |
|---|---|---|
| BetaDistributionNew(Double, Double) |
Constructs a new BetaDistribution using the
specified shape parameters.
|
| BetaDistributionNew(Double, Double, Double, Double) |
Constructs a new BetaDistribution using the
specified shape parameters.
|
| BetaDistributionNew(NumericalVariable, EstimationMethod) |
Constructs the beta distribution from a numerical variable.
|
| BetaDistributionNew(NumericalVariable) |
Constructs the beta distribution from a numerical variable.
|
Properties
| Icon | Type | Description |
|---|---|---|
 | Alpha |
Gets the first shape parameter of this BetaDistribution.
|
| Beta |
Gets the first shape parameter of this BetaDistribution.
|
| InterQuartileRange |
Returns the inter-quartile range of this distribution.
|
| IsSymmetrical |
Gets a value that indicates whether the distribution is known to be symmetrical around the mean.
|
| Kurtosis |
Gets the kurtosis of the distribution.
|
| LowerBound |
Gets the lower bound of the interval on which this BetaDistribution is defined.
|
| Mean |
Gets the mean or expectation value of the distribution.
|
| Skewness |
Gets the skewness of the distribution.
|
| StandardDeviation |
Gets the standard deviation of the distribution.
|
| UpperBound |
Gets the upper bound of the interval on which this BetaDistribution is defined.
|
| Variance |
Gets the variance of the distribution.
|
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 ContinuousUniformDistribution. If α=1 and β = 2, or α = 2 and β = 1, the beta distribution reduces to the TriangularDistribution.
Inheritance Hierarchy
System.Object
Extreme.Statistics.Distributions.Distribution
Extreme.Statistics.Distributions.ContinuousDistribution
Extreme.Statistics.Distributions.BetaDistribution
Extreme.Statistics.Distributions.Distribution
Extreme.Statistics.Distributions.ContinuousDistribution
Extreme.Statistics.Distributions.BetaDistribution
