public class BetaDistribution extends AbstractRealDistribution
Modifier and Type | Field and Description |
---|---|
static double |
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default 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
X whose values are distributed according
to this distribution, this method returns P(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, sample
public 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 evaluatedx
public 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 AbstractRealDistribution
x
- the point at which the PDF is evaluatedx
public 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 evaluatedx
protected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy
in class AbstractRealDistribution
public 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()
true
public 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 RealDistribution
sample
in class AbstractRealDistribution
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