Apache Commons Math 3.6.1 · org.apache.commons.math3.distribution.GammaDistribution

Field Summary

Modifier and Type	Field and Description
public static final double	DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy.
private final 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 final 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 final 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 final 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 final double	maxLogY Upper bound on `log(y)` (`y = x / scale`) for the selection of the computation method in `density(double)`.
private final double	minY Lower bound on `y = x / scale` for the selection of the computation method in `density(double)`.
private final double	scale The scale parameter.
private static final long	serialVersionUID Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID. Serializable version identifier.
private final double	shape The shape parameter.
private final double	shiftedShape The constant value of `shape + g + 0.5`, where `g` is the Lanczos constant `Gamma#LANCZOS_G`.
private final double	solverAbsoluteAccuracy Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy. Inverse cumulative probability accuracy.

Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:: random randomData SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Constructor Summary

Access	Constructor and Description
public	GammaDistribution(double the shape parameter shape, double the scale parameter scale) Creates a new gamma distribution with specified values of the shape and scale parameters.
public	GammaDistribution(double the shape parameter shape, double the scale parameter scale, double the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`). inverseCumAccuracy) Creates a new gamma distribution with specified values of the shape and scale parameters.
public	GammaDistribution(RandomGenerator Random number generator. rng, double the shape parameter shape, double the scale parameter scale) Creates a Gamma distribution.
public	GammaDistribution(RandomGenerator Random number generator. rng, double the shape parameter shape, double the scale parameter scale, double the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`). inverseCumAccuracy) Creates a Gamma distribution.

Method Summary

Modifier and Type	Method and Description
public double	cumulativeProbability(double the point at which the CDF is evaluated x) Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
public double	density(double the point at which the PDF is evaluated x) Implements org.apache.commons.math3.distribution.RealDistribution.density. Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`.
public double	Returns: the shape parameter getAlpha() Deprecated as of version 3.1, `getShape()` should be preferred. This method will be removed in version 4.0. Returns the shape parameter of `this` distribution.
public double	Returns: the scale parameter getBeta() Deprecated as of version 3.1, `getScale()` should be preferred. This method will be removed in version 4.0. Returns the scale parameter of `this` distribution.
public double	getNumericalMean() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean. Use this method to get the numerical value of the mean of this distribution.
public double	Returns: the variance (possibly `Double.POSITIVE_INFINITY` as for certain cases in `TDistribution`) or `Double.NaN` if it is not defined getNumericalVariance() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance. Use this method to get the numerical value of the variance of this distribution.
public double	Returns: the scale parameter getScale() Returns the scale parameter of `this` distribution.
public double	Returns: the shape parameter getShape() Returns the shape parameter of `this` distribution.
protected double	getSolverAbsoluteAccuracy() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy. Returns the solver absolute accuracy for inverse cumulative computation.
public double	Returns: lower bound of the support (always 0) getSupportLowerBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound. Access the lower bound of the support.
public double	Returns: upper bound of the support (always Double.POSITIVE_INFINITY) getSupportUpperBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound. Access the upper bound of the support.
public boolean	Returns: `true` isSupportConnected() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected. Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.
public boolean	isSupportLowerBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive. Whether or not the lower bound of support is in the domain of the density function.
public boolean	isSupportUpperBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive. Whether or not the upper bound of support is in the domain of the density function.
public double	logDensity(double the point at which the PDF is evaluated x) Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity. Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point `x`.
public double	Returns: random value sampled from the Gamma(shape, scale) distribution sample() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.sample. Implements org.apache.commons.math3.distribution.RealDistribution.sample. This implementation uses the following algorithms: For 0 < shape < 1: Ahrens, J.

Inherited from org.apache.commons.math3.distribution.AbstractRealDistribution:: cumulativeProbability inverseCumulativeProbability probability probability reseedRandomGenerator sample

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY	back to summary
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY Default inverse cumulative probability accuracy. Since 2.1

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

back to summary

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Default inverse cumulative probability accuracy.

Since: 2.1

densityPrefactor1	back to summary
private final 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)`. This prefactor is used in `density(double)`, when no overflow occurs with the natural calculation.

densityPrefactor2	back to summary
private final 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)`. This prefactor is used in `density(double)`, when overflow occurs with the natural calculation.

logDensityPrefactor1	back to summary
private final 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)`. This prefactor is used in `logDensity(double)`, when no overflow occurs with the natural calculation.

logDensityPrefactor2	back to summary
private final 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)`. This prefactor is used in `logDensity(double)`, when overflow occurs with the natural calculation.

maxLogY	back to summary
private final double maxLogY Upper bound on `log(y)` (`y = x / scale`) for the selection of the computation method in `density(double)`. For `log(y) >= maxLogY`, the natural calculation overflows.

minY	back to summary
private final double minY Lower bound on `y = x / scale` for the selection of the computation method in `density(double)`. For `y <= minY`, the natural calculation overflows.

scale	back to summary
private final double scale The scale parameter.

serialVersionUID	back to summary
private static final long serialVersionUID Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID. Serializable version identifier.

serialVersionUID

back to summary

private static final long serialVersionUID

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.serialVersionUID.

Serializable version identifier.

shape	back to summary
private final double shape The shape parameter.

shiftedShape	back to summary
private final double shiftedShape The constant value of `shape + g + 0.5`, where `g` is the Lanczos constant `Gamma#LANCZOS_G`.

solverAbsoluteAccuracy	back to summary
private final double solverAbsoluteAccuracy Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy. Inverse cumulative probability accuracy.

solverAbsoluteAccuracy

back to summary

private final double solverAbsoluteAccuracy

Hides org.apache.commons.math3.distribution.AbstractRealDistribution.solverAbsoluteAccuracy.

Inverse cumulative probability accuracy.

Constructor Detail

GammaDistribution back to summary

GammaDistribution	back to summary
public GammaDistribution(double shape, double scale) throws NotStrictlyPositiveException Creates a new gamma distribution with specified values of the shape and scale parameters. Note this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `sample()` and `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. Parameters shape:double the shape parameter scale:double the scale parameter Exceptions NotStrictlyPositiveException: if `shape <= 0` or `scale <= 0`.

public GammaDistribution(double shape, double scale) throws NotStrictlyPositiveException

Creates a new gamma distribution with specified values of the shape and scale parameters.

Note

this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see sample() and 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.

Parameters

shape:double: the shape parameter
scale:double: the scale parameter

Exceptions

NotStrictlyPositiveException:: if shape <= 0 or scale <= 0.

GammaDistribution back to summary

GammaDistribution	back to summary
public GammaDistribution(double shape, double scale, double inverseCumAccuracy) throws NotStrictlyPositiveException Creates a new gamma distribution with specified values of the shape and scale parameters. Note this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `sample()` and `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. Parameters shape:double the shape parameter scale:double the scale parameter inverseCumAccuracy:double the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`). Exceptions NotStrictlyPositiveException: if `shape <= 0` or `scale <= 0`. Since 2.1

public GammaDistribution(double shape, double scale, double inverseCumAccuracy) throws NotStrictlyPositiveException

Creates a new gamma distribution with specified values of the shape and scale parameters.

Note

Parameters

shape:double: the shape parameter
scale:double: the scale parameter
inverseCumAccuracy:double: the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Exceptions

NotStrictlyPositiveException:: if shape <= 0 or scale <= 0.

Since

2.1

GammaDistribution back to summary

GammaDistribution	back to summary
public GammaDistribution(RandomGenerator rng, double shape, double scale) throws NotStrictlyPositiveException Creates a Gamma distribution. Parameters rng:RandomGenerator Random number generator. shape:double the shape parameter scale:double the scale parameter Exceptions NotStrictlyPositiveException: if `shape <= 0` or `scale <= 0`. Since 3.3

public GammaDistribution(RandomGenerator rng, double shape, double scale) throws NotStrictlyPositiveException

Creates a Gamma distribution.

Parameters

rng:RandomGenerator: Random number generator.
shape:double: the shape parameter
scale:double: the scale parameter

Exceptions

NotStrictlyPositiveException:: if shape <= 0 or scale <= 0.

Since

3.3

GammaDistribution back to summary

GammaDistribution	back to summary
public GammaDistribution(RandomGenerator rng, double shape, double scale, double inverseCumAccuracy) throws NotStrictlyPositiveException Creates a Gamma distribution. Parameters rng:RandomGenerator Random number generator. shape:double the shape parameter scale:double the scale parameter inverseCumAccuracy:double the maximum absolute error in inverse cumulative probability estimates (defaults to `DEFAULT_INVERSE_ABSOLUTE_ACCURACY`). Exceptions NotStrictlyPositiveException: if `shape <= 0` or `scale <= 0`. Since 3.1

public GammaDistribution(RandomGenerator rng, double shape, double scale, double inverseCumAccuracy) throws NotStrictlyPositiveException

Creates a Gamma distribution.

Parameters

rng:RandomGenerator: Random number generator.
shape:double: the shape parameter
scale:double: the scale parameter
inverseCumAccuracy:double: the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).

Exceptions

NotStrictlyPositiveException:: if shape <= 0 or scale <= 0.

Since

3.1

Method Detail

cumulativeProbability back to summary

cumulativeProbability	back to summary
public double cumulativeProbability(double x) Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability. For a random variable `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: Chi-Squared Distribution, equation (9). Casella, G., & Berger, R. (1990). Statistical Inference. Belmont, CA: Duxbury Press. Parameters x:double the point at which the CDF is evaluated Returns:double the probability that a random variable with this distribution takes a value less than or equal to `x`

public double cumulativeProbability(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

Doc from org.apache.commons.math3.distribution.RealDistribution.cumulativeProbability.

For a random variable 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:

Chi-Squared Distribution, equation (9).
Casella, G., & Berger, R. (1990). Statistical Inference. Belmont, CA: Duxbury Press.

Parameters

x:double: the point at which the CDF is evaluated

Returns:double

the probability that a random variable with this distribution takes a value less than or equal to x

density back to summary

density	back to summary
public double density(double x) Implements org.apache.commons.math3.distribution.RealDistribution.density. Doc from org.apache.commons.math3.distribution.RealDistribution.density. Returns the probability density function (PDF) of this distribution evaluated at the specified point `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. Parameters x:double the point at which the PDF is evaluated Returns:double the value of the probability density function at point `x`

public double density(double x)

Implements org.apache.commons.math3.distribution.RealDistribution.density.

Doc from org.apache.commons.math3.distribution.RealDistribution.density.

Returns the probability density function (PDF) of this distribution evaluated at the specified point 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.

Parameters

x:double: the point at which the PDF is evaluated

Returns:double

the value of the probability density function at point x

getAlpha back to summary

getAlpha	back to summary
public double getAlpha() Deprecated as of version 3.1, `getShape()` should be preferred. This method will be removed in version 4.0. Returns the shape parameter of `this` distribution. Returns:double the shape parameter Annotations @Deprecated

public double getAlpha()

Deprecated

as of version 3.1, getShape() should be preferred. This method will be removed in version 4.0.

Returns the shape parameter of this distribution.

Returns:double

the shape parameter

Annotations

@Deprecated

getBeta back to summary

getBeta	back to summary
public double getBeta() Deprecated as of version 3.1, `getScale()` should be preferred. This method will be removed in version 4.0. Returns the scale parameter of `this` distribution. Returns:double the scale parameter Annotations @Deprecated

public double getBeta()

Deprecated

as of version 3.1, getScale() should be preferred. This method will be removed in version 4.0.

Returns the scale parameter of this distribution.

Returns:double

the scale parameter

Annotations

@Deprecated

getNumericalMean back to summary

getNumericalMean	back to summary
public double getNumericalMean() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean. Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalMean. Use this method to get the numerical value of the mean of this distribution. For shape parameter `alpha` and scale parameter `beta`, the mean is `alpha * beta`. Returns:double the mean or `Double.NaN` if it is not defined

public double getNumericalMean()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalMean.

Use this method to get the numerical value of the mean of this distribution. For shape parameter alpha and scale parameter beta, the mean is alpha * beta.

Returns:double: the mean or Double.NaN if it is not defined

getNumericalVariance back to summary

getNumericalVariance	back to summary
public double getNumericalVariance() Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance. Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance. Use this method to get the numerical value of the variance of this distribution. For shape parameter `alpha` and scale parameter `beta`, the variance is `alpha * beta^2`. Returns:double the variance (possibly `Double.POSITIVE_INFINITY` as for certain cases in `TDistribution`) or `Double.NaN` if it is not defined

public double getNumericalVariance()

Implements org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Doc from org.apache.commons.math3.distribution.RealDistribution.getNumericalVariance.

Use this method to get the numerical value of the variance of this distribution. For shape parameter alpha and scale parameter beta, the variance is alpha * beta^2.

Returns:double: the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getScale back to summary

getScale	back to summary
public double getScale() Returns the scale parameter of `this` distribution. Returns:double the scale parameter Since 3.1

public double getScale()

Returns the scale parameter of this distribution.

Returns:double: the scale parameter
Since: 3.1

getShape back to summary

getShape	back to summary
public double getShape() Returns the shape parameter of `this` distribution. Returns:double the shape parameter Since 3.1

public double getShape()

Returns the shape parameter of this distribution.

Returns:double: the shape parameter
Since: 3.1

getSolverAbsoluteAccuracy	back to summary
protected double getSolverAbsoluteAccuracy() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy. Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default. Returns:double the maximum absolute error in inverse cumulative probability estimates Annotations @Override

getSolverAbsoluteAccuracy

back to summary

protected double getSolverAbsoluteAccuracy()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.getSolverAbsoluteAccuracy.

Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Returns:double

the maximum absolute error in inverse cumulative probability estimates

Annotations

@Override

getSupportLowerBound back to summary

getSupportLowerBound	back to summary
public double getSupportLowerBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound. Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound. Access the lower bound of the support. This method must return the same value as `inverseCumulativeProbability(0)`. In other words, this method must return `inf {x in R \| P(X <= x) > 0}`. The lower bound of the support is always 0 no matter the parameters. Returns:double lower bound of the support (always 0)

public double getSupportLowerBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportLowerBound.

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always 0 no matter the parameters.

Returns:double: lower bound of the support (always 0)

getSupportUpperBound back to summary

getSupportUpperBound	back to summary
public double getSupportUpperBound() Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound. Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound. Access the upper bound of the support. This method must return the same value as `inverseCumulativeProbability(1)`. In other words, this method must return `inf {x in R \| P(X <= x) = 1}`. The upper bound of the support is always positive infinity no matter the parameters. Returns:double upper bound of the support (always Double.POSITIVE_INFINITY)

public double getSupportUpperBound()

Implements org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Doc from org.apache.commons.math3.distribution.RealDistribution.getSupportUpperBound.

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always positive infinity no matter the parameters.

Returns:double: upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportConnected back to summary

isSupportConnected	back to summary
public boolean isSupportConnected() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected. Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportConnected. Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected. Returns:boolean `true`

public boolean isSupportConnected()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportConnected.

Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportConnected.

Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:boolean: true

isSupportLowerBoundInclusive back to summary

isSupportLowerBoundInclusive	back to summary
public boolean isSupportLowerBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive. Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive. Whether or not the lower bound of support is in the domain of the density function. Returns true iff `getSupporLowerBound()` is finite and `density(getSupportLowerBound())` returns a non-NaN, non-infinite value. Returns:boolean true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

public boolean isSupportLowerBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportLowerBoundInclusive.

Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.

Returns:boolean: true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there

isSupportUpperBoundInclusive back to summary

isSupportUpperBoundInclusive	back to summary
public boolean isSupportUpperBoundInclusive() Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive. Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive. Whether or not the upper bound of support is in the domain of the density function. Returns true iff `getSupportUpperBound()` is finite and `density(getSupportUpperBound())` returns a non-NaN, non-infinite value. Returns:boolean true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

public boolean isSupportUpperBoundInclusive()

Implements org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Doc from org.apache.commons.math3.distribution.RealDistribution.isSupportUpperBoundInclusive.

Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.

Returns:boolean: true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there

logDensity back to summary

logDensity	back to summary
public double logDensity(double x) Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity. Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity. Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point `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 `density(double)`. The default implementation simply computes the logarithm of `density(x)`. Parameters x:double the point at which the PDF is evaluated Returns:double the logarithm of the value of the probability density function at point `x` Annotations @Override

public double logDensity(double x)

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity.

Doc from org.apache.commons.math3.distribution.AbstractRealDistribution.logDensity.

Returns the natural logarithm of the probability density function (PDF) of this distribution evaluated at the specified point 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 density(double). The default implementation simply computes the logarithm of density(x).

Parameters

x:double: the point at which the PDF is evaluated

Returns:double

the logarithm of the value of the probability density function at point x

Annotations

@Override

sample	back to summary
public double sample() Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.sample. Implements org.apache.commons.math3.distribution.RealDistribution.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. Returns:double random value sampled from the Gamma(shape, scale) distribution Annotations @Override

sample

back to summary

public double sample()

Overrides org.apache.commons.math3.distribution.AbstractRealDistribution.sample.

Implements org.apache.commons.math3.distribution.RealDistribution.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.

Returns:double

random value sampled from the Gamma(shape, scale) distribution

Annotations

@Override

public Class GammaDistribution

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