public class GammaDistribution extends AbstractRealDistribution
Modifier and Type | Field and Description |
---|---|
static double |
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
|
private double |
densityPrefactor1
The constant value of
shape / scale * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape) ,
where L(shape) is the Lanczos approximation returned by
Gamma.lanczos(double) . |
private double |
densityPrefactor2
The constant value of
shape * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape) ,
where L(shape) is the Lanczos approximation returned by
Gamma.lanczos(double) . |
private double |
logDensityPrefactor1
The constant value of
log(shape / scale * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape)) ,
where L(shape) is the Lanczos approximation returned by
Gamma.lanczos(double) . |
private double |
logDensityPrefactor2
The constant value of
log(shape * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape)) ,
where L(shape) is the Lanczos approximation returned by
Gamma.lanczos(double) . |
private double |
maxLogY
Upper bound on
log(y) (y = x / scale ) for the selection
of the computation method in density(double) . |
private double |
minY
Lower bound on
y = x / scale for the selection of the computation
method in density(double) . |
private double |
scale
The scale parameter.
|
private static long |
serialVersionUID
Serializable version identifier.
|
private double |
shape
The shape parameter.
|
private double |
shiftedShape
|
private double |
solverAbsoluteAccuracy
Inverse cumulative probability accuracy.
|
random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
Constructor and Description |
---|
GammaDistribution(double shape,
double scale)
Creates a new gamma distribution with specified values of the shape and
scale parameters.
|
GammaDistribution(double shape,
double scale,
double inverseCumAccuracy)
Creates a new gamma distribution with specified values of the shape and
scale parameters.
|
GammaDistribution(RandomGenerator rng,
double shape,
double scale)
Creates a Gamma distribution.
|
GammaDistribution(RandomGenerator rng,
double shape,
double scale,
double inverseCumAccuracy)
Creates a Gamma 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()
Deprecated.
as of version 3.1,
getShape() should be preferred.
This method will be removed in version 4.0. |
double |
getBeta()
Deprecated.
as of version 3.1,
getScale() should be preferred.
This method will be removed in version 4.0. |
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.
|
double |
getScale()
Returns the scale parameter of
this distribution. |
double |
getShape()
Returns the shape parameter of
this distribution. |
protected double |
getSolverAbsoluteAccuracy()
Returns the solver absolute accuracy for inverse cumulative computation.
|
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()
This implementation uses the following algorithms:
|
cumulativeProbability, inverseCumulativeProbability, probability, probability, reseedRandomGenerator, sample
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
private static final long serialVersionUID
private final double shape
private final double scale
private final double shiftedShape
private final double densityPrefactor1
shape / scale * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape)
,
where L(shape)
is the Lanczos approximation returned by
Gamma.lanczos(double)
. This prefactor is used in
density(double)
, when no overflow occurs with the natural
calculation.private final double logDensityPrefactor1
log(shape / scale * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape))
,
where L(shape)
is the Lanczos approximation returned by
Gamma.lanczos(double)
. This prefactor is used in
logDensity(double)
, when no overflow occurs with the natural
calculation.private final double densityPrefactor2
shape * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape)
,
where L(shape)
is the Lanczos approximation returned by
Gamma.lanczos(double)
. This prefactor is used in
density(double)
, when overflow occurs with the natural
calculation.private final double logDensityPrefactor2
log(shape * sqrt(e / (2 * pi * (shape + g + 0.5))) / L(shape))
,
where L(shape)
is the Lanczos approximation returned by
Gamma.lanczos(double)
. This prefactor is used in
logDensity(double)
, when overflow occurs with the natural
calculation.private final double minY
y = x / scale
for the selection of the computation
method in density(double)
. For y <= minY
, the natural
calculation overflows.private final double maxLogY
log(y)
(y = x / scale
) for the selection
of the computation method in density(double)
. For
log(y) >= maxLogY
, the natural calculation overflows.private final double solverAbsoluteAccuracy
public GammaDistribution(double shape, double scale) throws NotStrictlyPositiveException
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.
shape
- the shape parameterscale
- the scale parameterNotStrictlyPositiveException
- if shape <= 0
or
scale <= 0
.public GammaDistribution(double shape, double scale, double inverseCumAccuracy) throws NotStrictlyPositiveException
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.
shape
- the shape parameterscale
- the scale parameterinverseCumAccuracy
- the maximum absolute error in inverse
cumulative probability estimates (defaults to
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).NotStrictlyPositiveException
- if shape <= 0
or
scale <= 0
.public GammaDistribution(RandomGenerator rng, double shape, double scale) throws NotStrictlyPositiveException
rng
- Random number generator.shape
- the shape parameterscale
- the scale parameterNotStrictlyPositiveException
- if shape <= 0
or
scale <= 0
.public GammaDistribution(RandomGenerator rng, double shape, double scale, double inverseCumAccuracy) throws NotStrictlyPositiveException
rng
- Random number generator.shape
- the shape parameterscale
- the scale parameterinverseCumAccuracy
- the maximum absolute error in inverse
cumulative probability estimates (defaults to
DEFAULT_INVERSE_ABSOLUTE_ACCURACY
).NotStrictlyPositiveException
- if shape <= 0
or
scale <= 0
.@Deprecated public double getAlpha()
getShape()
should be preferred.
This method will be removed in version 4.0.this
distribution.public double getShape()
this
distribution.@Deprecated public double getBeta()
getScale()
should be preferred.
This method will be removed in version 4.0.this
distribution.public double getScale()
this
distribution.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.
The implementation of this method is based on:
x
- the point at which the CDF is evaluatedx
protected double getSolverAbsoluteAccuracy()
getSolverAbsoluteAccuracy
in class AbstractRealDistribution
public double getNumericalMean()
alpha
and scale parameter beta
, the
mean is alpha * beta
.Double.NaN
if it is not definedpublic double getNumericalVariance()
alpha
and scale parameter beta
, the
variance is alpha * beta^2
.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()
This implementation uses the following algorithms:
For 0 < shape < 1:
Ahrens, J. H. and Dieter, U., Computer methods for
sampling from gamma, beta, Poisson and binomial distributions.
Computing, 12, 223-246, 1974.
For shape >= 1:
Marsaglia and Tsang, A Simple Method for Generating
Gamma Variables. ACM Transactions on Mathematical Software,
Volume 26 Issue 3, September, 2000.
sample
in interface RealDistribution
sample
in class AbstractRealDistribution