GammaDistribution (ELKI: Environment for DeveLoping KDD-Applications Supported by Index-Structures)

java.lang.Object
- de.lmu.ifi.dbs.elki.math.statistics.distribution.GammaDistribution

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

ChiSquaredDistribution
```
public class GammaDistribution
extends Object
implements Distribution
```
Gamma Distribution, with random generation and density functions.

Field Summary

Fields
Modifier and Type	Field and Description
`private double`	`k` Alpha == k
`(package private) static double[]`	`LANCZOS` LANCZOS-Coefficients for Gamma approximation.
`(package private) static double`	`NUM_PRECISION` Numerical precision to use
`private Random`	`random` The random generator.
`private double`	`theta` Theta == 1 / Beta

Constructor Summary

Constructors
Constructor and Description
`GammaDistribution(double k, double theta)` Constructor for Gamma distribution.
`GammaDistribution(double k, double theta, Random random)` Constructor for Gamma distribution.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`cdf(double val)` Return the cumulative density function at the given value.
`static double`	`cdf(double val, double k, double theta)` The CDF, static version.
`double`	`getK()`
`double`	`getTheta()`
`static double`	`logGamma(double x)` Compute logGamma.
`double`	`nextRandom()` Generate a new random value
`static double`	`nextRandom(double k, double theta, Random random)` Generate a random value with the generators parameters.
`double`	`pdf(double val)` Return the density of an existing value
`static double`	`pdf(double x, double k, double theta)` Gamma distribution PDF (with 0.0 for x < 0)
`static double`	`regularizedGammaP(double a, double x)` Returns the regularized gamma function P(a, x).
`static double`	`regularizedGammaQ(double a, double x)` Returns the regularized gamma function Q(a, x) = 1 - P(a, x).
`String`	`toString()` Simple toString explaining the distribution parameters.

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

- Field Detail
  - LANCZOS
```
static final double[] LANCZOS
```
    LANCZOS-Coefficients for Gamma approximation. These are said to have higher precision than those in "Numerical Recipes". They probably come from Paul Godfrey: http://my.fit.edu/~gabdo/gamma.txt
  - NUM_PRECISION
```
static final double NUM_PRECISION
```
    Numerical precision to use
    
    See Also:
    Constant Field Values
  - k
```
private final double k
```
    Alpha == k
  - theta
```
private final double theta
```
    Theta == 1 / Beta
  - random
```
private Random random
```
    The random generator.
- Constructor Detail
  - GammaDistribution
```
public GammaDistribution(double k,
                 double theta,
                 Random random)
```
    Constructor for Gamma distribution.
    
    Parameters:
    k - k, alpha aka. "shape" parameter
    theta - Theta = 1.0/Beta aka. "scaling" parameter
    random - Random generator
  - GammaDistribution
```
public GammaDistribution(double k,
                 double theta)
```
    Constructor for Gamma distribution.
    
    Parameters:
    k - k, alpha aka. "shape" parameter
    theta - Theta = 1.0/Beta aka. "scaling" parameter
- Method Detail
  - pdf
```
public double pdf(double val)
```
    Description copied from interface: Distribution
    
    Return the density of an existing value
    
    Specified by:
    
    pdf in interface Distribution
    
    Parameters:
    val - existing value
    
    Returns:
    distribution density
  - cdf
```
public double cdf(double val)
```
    Description copied from interface: Distribution
    
    Return the cumulative density function at the given value.
    
    Specified by:
    
    cdf in interface Distribution
    
    Parameters:
    val - existing value
    
    Returns:
    cumulative density
  - nextRandom
```
public double nextRandom()
```
    Description copied from interface: Distribution
    
    Generate a new random value
    
    Specified by:
    
    nextRandom in interface Distribution
    
    Returns:
    new random value
  - toString
```
public String toString()
```
    Simple toString explaining the distribution parameters. Used in producing a model description.
    
    Specified by:
    
    toString in interface Distribution
    
    Overrides:
    
    toString in class Object
    
    Returns:
    description
  - getK
```
public double getK()
```
    Returns:
    the value of k
  - getTheta
```
public double getTheta()
```
    Returns:
    the standard deviation
  - cdf
```
public static double cdf(double val,
         double k,
         double theta)
```
    The CDF, static version.
    
    Parameters:
    val - Value
    k - Shape k
    theta - Theta = 1.0/Beta aka. "scaling" parameter
    
    Returns:
    cdf value
  - pdf
```
public static double pdf(double x,
         double k,
         double theta)
```
    Gamma distribution PDF (with 0.0 for x < 0)
    
    Parameters:
    x - query value
    k - Alpha
    theta - Theta = 1 / Beta
    
    Returns:
    probability density
  - logGamma
```
public static double logGamma(double x)
```
    Compute logGamma. Based loosely on "Numerical Recpies" and the work of Paul Godfrey at http://my.fit.edu/~gabdo/gamma.txt TODO: find out which approximation really is the best...
    
    Parameters:
    x - Parameter x
    
    Returns:
    log(Γ(x))
  - regularizedGammaP
```
public static double regularizedGammaP(double a,
                       double x)
```
    Returns the regularized gamma function P(a, x). Includes the quadrature way of computing. TODO: find "the" most accurate version of this. We seem to agree with others for the first 10+ digits, but diverge a bit later than that.
    
    Parameters:
    a - Parameter a
    x - Parameter x
    
    Returns:
    Gamma value
  - regularizedGammaQ
```
public static double regularizedGammaQ(double a,
                       double x)
```
    Returns the regularized gamma function Q(a, x) = 1 - P(a, x). Includes the continued fraction way of computing, based loosely on the book "Numerical Recipes"; but probably not with the exactly same precision, since we reimplemented this in our coding style, not literally. TODO: find "the" most accurate version of this. We seem to agree with others for the first 10+ digits, but diverge a bit later than that.
    
    Parameters:
    a - parameter a
    x - parameter x
    
    Returns:
    Result
  - nextRandom
```
public static double nextRandom(double k,
                double theta,
                Random random)
```
    Generate a random value with the generators parameters. Along the lines of - J.H. Ahrens, U. Dieter (1974): Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing 12, 223-246. - J.H. Ahrens, U. Dieter (1982): Generating gamma variates by a modified rejection technique, Communications of the ACM 25, 47-54.
    
    Parameters:
    k - K parameter
    theta - Theta parameter
    random - Random generator

Class GammaDistribution

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

LANCZOS

NUM_PRECISION

k

theta

random

Constructor Detail

GammaDistribution

GammaDistribution

Method Detail

pdf

cdf

nextRandom

toString

getK

getTheta

cdf

pdf

logGamma

regularizedGammaP

regularizedGammaQ

nextRandom