GammaDistribution (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.distribution.AbstractRealDistribution
- - org.apache.commons.math3.distribution.GammaDistribution

All Implemented Interfaces:

Serializable, RealDistribution
```
public class GammaDistribution
extends AbstractRealDistribution
```
Implementation of the Gamma distribution.

See Also:
Gamma distribution (Wikipedia), Gamma distribution (MathWorld), Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
- Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
  random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY

Fields
Modifier and Type	Field and Description
`static double`	`DEFAULT_INVERSE_ABSOLUTE_ACCURACY` Default inverse cumulative probability accuracy.

Constructor Summary

Constructors
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.

Method Summary

Methods
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:

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
cumulativeProbability, inverseCumulativeProbability, probability, probability, reseedRandomGenerator, sample

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - DEFAULT_INVERSE_ABSOLUTE_ACCURACY
```
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
```
    Default inverse cumulative probability accuracy.
    
    Since:
    
    2.1
    
    See Also:
    Constant Field Values
- Constructor Detail
  - GammaDistribution
```
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 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.
    
    Parameters:
    shape - the shape parameter
    scale - the scale parameter
    
    Throws:
    
    NotStrictlyPositiveException - if shape <= 0 or scale <= 0.
  - GammaDistribution
```
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 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.
    
    Parameters:
    shape - the shape parameter
    scale - the scale parameter
    inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
    
    Throws:
    
    NotStrictlyPositiveException - if shape <= 0 or scale <= 0.
    Since:
    
    2.1
  - GammaDistribution
```
public GammaDistribution(RandomGenerator rng,
                 double shape,
                 double scale)
                  throws NotStrictlyPositiveException
```
    Creates a Gamma distribution.
    
    Parameters:
    rng - Random number generator.
    shape - the shape parameter
    scale - the scale parameter
    
    Throws:
    
    NotStrictlyPositiveException - if shape <= 0 or scale <= 0.
    Since:
    
    3.3
  - GammaDistribution
```
public GammaDistribution(RandomGenerator rng,
                 double shape,
                 double scale,
                 double inverseCumAccuracy)
                  throws NotStrictlyPositiveException
```
    Creates a Gamma distribution.
    
    Parameters:
    rng - Random number generator.
    shape - the shape parameter
    scale - the scale parameter
    inverseCumAccuracy - the maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
    
    Throws:
    
    NotStrictlyPositiveException - if shape <= 0 or scale <= 0.
    Since:
    
    3.1
- Method Detail
  - getAlpha
```
@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:
    the shape parameter
  - getShape
```
public double getShape()
```
    Returns the shape parameter of this distribution.
    
    Returns:
    the shape parameter
    Since:
    
    3.1
  - getBeta
```
@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:
    the scale parameter
  - getScale
```
public double getScale()
```
    Returns the scale parameter of this distribution.
    
    Returns:
    the scale parameter
    Since:
    
    3.1
  - density
```
public double density(double x)
```
    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 - the point at which the PDF is evaluated
    
    Returns:
    the value of the probability density function at point x
  - logDensity
```
public double logDensity(double x)
```
    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 RealDistribution.density(double). The default implementation simply computes the logarithm of density(x).
    
    Overrides:
    
    logDensity in class AbstractRealDistribution
    
    Parameters:
    x - the point at which the PDF is evaluated
    
    Returns:
    the logarithm of the value of the probability density function at point x
  - cumulativeProbability
```
public double cumulativeProbability(double x)
```
    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 - the point at which the CDF is evaluated
    
    Returns:
    the probability that a random variable with this distribution takes a value less than or equal to x
  - getSolverAbsoluteAccuracy
```
protected double 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.
    
    Overrides:
    
    getSolverAbsoluteAccuracy in class AbstractRealDistribution
    
    Returns:
    the maximum absolute error in inverse cumulative probability estimates
  - getNumericalMean
```
public double 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:
    the mean or Double.NaN if it is not defined
  - getNumericalVariance
```
public double 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:
    the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined
  - getSupportLowerBound
```
public double 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:
    lower bound of the support (always 0)
  - getSupportUpperBound
```
public double 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:
    upper bound of the support (always Double.POSITIVE_INFINITY)
  - isSupportLowerBoundInclusive
```
public boolean 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:
    true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there
  - isSupportUpperBoundInclusive
```
public boolean 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:
    true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there
  - isSupportConnected
```
public boolean 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:
    true
  - sample
```
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.
    
    Specified by:
    
    sample in interface RealDistribution
    
    Overrides:
    
    sample in class AbstractRealDistribution
    
    Returns:
    random value sampled from the Gamma(shape, scale) distribution

Class GammaDistribution

Field Summary

Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

Constructor Summary

Method Summary

Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Constructor Detail

GammaDistribution

GammaDistribution

GammaDistribution

GammaDistribution

Method Detail

getAlpha

getShape

getBeta

getScale

density

logDensity

cumulativeProbability

getSolverAbsoluteAccuracy

getNumericalMean

getNumericalVariance

getSupportLowerBound

getSupportUpperBound

isSupportLowerBoundInclusive

isSupportUpperBoundInclusive

isSupportConnected

sample