public class BetaDistribution extends AbstractRealDistribution
| Modifier and Type | Field and Description | 
|---|---|
| static double | DEFAULT_INVERSE_ABSOLUTE_ACCURACYDefault inverse cumulative probability accuracy. | 
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY| Constructor and Description | 
|---|
| BetaDistribution(double alpha,
                double beta)Build a new instance. | 
| BetaDistribution(double alpha,
                double beta,
                double inverseCumAccuracy)Build a new instance. | 
| BetaDistribution(RandomGenerator rng,
                double alpha,
                double beta)Creates a β distribution. | 
| BetaDistribution(RandomGenerator rng,
                double alpha,
                double beta,
                double inverseCumAccuracy)Creates a β distribution. | 
| Modifier and Type | Method and Description | 
|---|---|
| double | cumulativeProbability(double x)For a random variable  Xwhose values are distributed according
 to this distribution, this method returnsP(X <= x). | 
| double | density(double x)Returns the probability density function (PDF) of this distribution
 evaluated at the specified point  x. | 
| double | getAlpha()Access the first shape parameter,  alpha. | 
| double | getBeta()Access the second shape parameter,  beta. | 
| double | getNumericalMean()Use this method to get the numerical value of the mean of this
 distribution. | 
| double | getNumericalVariance()Use this method to get the numerical value of the variance of this
 distribution. | 
| protected double | getSolverAbsoluteAccuracy()Return the absolute accuracy setting of the solver used to estimate
 inverse cumulative probabilities. | 
| double | getSupportLowerBound()Access the lower bound of the support. | 
| double | getSupportUpperBound()Access the upper bound of the support. | 
| boolean | isSupportConnected()Use this method to get information about whether the support is connected,
 i.e. | 
| boolean | isSupportLowerBoundInclusive()Whether or not the lower bound of support is in the domain of the density
 function. | 
| boolean | isSupportUpperBoundInclusive()Whether or not the upper bound of support is in the domain of the density
 function. | 
| double | logDensity(double x)Returns the natural logarithm of the probability density function (PDF) of this distribution
 evaluated at the specified point  x. | 
| double | sample()Generate a random value sampled from this distribution. | 
cumulativeProbability, inverseCumulativeProbability, probability, probability, reseedRandomGenerator, samplepublic static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
public BetaDistribution(double alpha,
                double beta)
 Note: this constructor will implicitly create an instance of
 Well19937c as random generator to be used for sampling only (see
 sample() and AbstractRealDistribution.sample(int)). In case no sampling is
 needed for the created distribution, it is advised to pass null
 as random generator via the appropriate constructors to avoid the
 additional initialisation overhead.
alpha - First shape parameter (must be positive).beta - Second shape parameter (must be positive).public BetaDistribution(double alpha,
                double beta,
                double inverseCumAccuracy)
 Note: this constructor will implicitly create an instance of
 Well19937c as random generator to be used for sampling only (see
 sample() and AbstractRealDistribution.sample(int)). In case no sampling is
 needed for the created distribution, it is advised to pass null
 as random generator via the appropriate constructors to avoid the
 additional initialisation overhead.
alpha - First shape parameter (must be positive).beta - Second shape parameter (must be positive).inverseCumAccuracy - Maximum absolute error in inverse
 cumulative probability estimates (defaults to
 DEFAULT_INVERSE_ABSOLUTE_ACCURACY).public BetaDistribution(RandomGenerator rng, double alpha, double beta)
rng - Random number generator.alpha - First shape parameter (must be positive).beta - Second shape parameter (must be positive).public BetaDistribution(RandomGenerator rng, double alpha, double beta, double inverseCumAccuracy)
rng - Random number generator.alpha - First shape parameter (must be positive).beta - Second shape parameter (must be positive).inverseCumAccuracy - Maximum absolute error in inverse
 cumulative probability estimates (defaults to
 DEFAULT_INVERSE_ABSOLUTE_ACCURACY).public double getAlpha()
alpha.public double getBeta()
beta.public double density(double x)
x. In general, the PDF is
 the derivative of the CDF.
 If the derivative does not exist at x, then an appropriate
 replacement should be returned, e.g. Double.POSITIVE_INFINITY,
 Double.NaN, or  the limit inferior or limit superior of the
 difference quotient.x - the point at which the PDF is evaluatedxpublic double logDensity(double x)
x. In general, the PDF is the derivative of the
 CDF. If the derivative does not exist at x,
 then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY,
 Double.NaN, or the limit inferior or limit superior of the difference quotient. Note
 that due to the floating point precision and under/overflow issues, this method will for some
 distributions be more precise and faster than computing the logarithm of
 RealDistribution.density(double). The default implementation simply computes the logarithm of
 density(x).logDensity in class AbstractRealDistributionx - the point at which the PDF is evaluatedxpublic double cumulativeProbability(double x)
X whose values are distributed according
 to this distribution, this method returns P(X <= x). In other
 words, this method represents the (cumulative) distribution function
 (CDF) for this distribution.x - the point at which the CDF is evaluatedxprotected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy in class AbstractRealDistributionpublic double getNumericalMean()
alpha and second shape parameter
 beta, the mean is alpha / (alpha + beta).Double.NaN if it is not definedpublic double getNumericalVariance()
alpha and second shape parameter
 beta, the variance is
 (alpha * beta) / [(alpha + beta)^2 * (alpha + beta + 1)].Double.POSITIVE_INFINITY as
 for certain cases in TDistribution) or Double.NaN if it
 is not definedpublic double getSupportLowerBound()
inverseCumulativeProbability(0). In other words, this
 method must return
 inf {x in R | P(X <= x) > 0}.
public double getSupportUpperBound()
inverseCumulativeProbability(1). In other words, this
 method must return
 inf {x in R | P(X <= x) = 1}.
public boolean isSupportLowerBoundInclusive()
getSupporLowerBound() is finite and
 density(getSupportLowerBound()) returns a non-NaN, non-infinite
 value.public boolean isSupportUpperBoundInclusive()
getSupportUpperBound() is finite and
 density(getSupportUpperBound()) returns a non-NaN, non-infinite
 value.public boolean isSupportConnected()
truepublic double sample()
Sampling is performed using Cheng algorithms:
R. C. H. Cheng, "Generating beta variates with nonintegral shape parameters.". Communications of the ACM, 21, 317–322, 1978.
sample in interface RealDistributionsample in class AbstractRealDistributionCopyright © 2003–2016 The Apache Software Foundation. All rights reserved.