com.numericalmethod.suanshu.stats.regression.linear.glm.quasi.family
Class Gamma

java.lang.Object
  com.numericalmethod.suanshu.stats.regression.linear.glm.distribution.Family
      com.numericalmethod.suanshu.stats.regression.linear.glm.distribution.Gamma
          com.numericalmethod.suanshu.stats.regression.linear.glm.quasi.family.Gamma

All Implemented Interfaces:

ExponentialDistribution, QuasiFamily

public class Gamma
extends Gamma
implements QuasiFamily

The quasi Gamma family of GLM.

Constructor Summary

Gamma()
Create an instance of Gamma.

Gamma(LinkFunction link)
Create an instance of Gamma with an overriding link function.

Method Summary

Family	asFamily()
double	quasiDeviance(double y, double mu) the quasi-deviance function corresponding to a single observation
double	quasiLikelihood(double mu, double y) the quasi-likelihood function corresponding to a single observation Q(μ; y)

Methods inherited from class com.numericalmethod.suanshu.stats.regression.linear.glm.distribution.Gamma

AIC, cumulant, deviance, dispersion, overdispersion, theta, variance

Methods inherited from class com.numericalmethod.suanshu.stats.regression.linear.glm.distribution.Family

link

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface com.numericalmethod.suanshu.stats.regression.linear.glm.quasi.family.QuasiFamily

link

Methods inherited from interface com.numericalmethod.suanshu.stats.regression.linear.glm.distribution.ExponentialDistribution

AIC, cumulant, deviance, dispersion, overdispersion, theta, variance

Constructor Detail

Gamma

public Gamma()

Create an instance of Gamma. The canonical link is Inverse.

See Also:

"pp.32. Section 2.2.4. Measuring the goodness-of-fit. Generalized Linear Models. 2nd ed. P. J. MacCullagh and J. A. Nelder."

Gamma

public Gamma(LinkFunction link)

Create an instance of Gamma with an overriding link function.

Parameters:

link - the overriding link function

Method Detail

quasiLikelihood

public double quasiLikelihood(double mu,
                              double y)

Description copied from interface: QuasiFamily

the quasi-likelihood function corresponding to a single observation Q(μ; y)

Specified by:

quasiLikelihood in interface QuasiFamily

Parameters:

mu - μ

y - y

Returns:

Q(μ; y)

See Also:

"P. J. MacCullagh and J. A. Nelder, Generalized Linear Models, 2nd ed. Chapter 9. Table 9.1. p.326."

quasiDeviance

public double quasiDeviance(double y,
                            double mu)

Description copied from interface: QuasiFamily

the quasi-deviance function corresponding to a single observation

Specified by:

quasiDeviance in interface QuasiFamily

Parameters:

y - y

mu - μ

Returns:

D(y; μ;)

See Also:

"P. J. MacCullagh and J. A. Nelder, Generalized Linear Models, 2nd ed. Chapter 9. Eq. 9.4., the integral form, p.327."

asFamily

public Family asFamily()

Specified by:

asFamily in interface QuasiFamily