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

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

All Implemented Interfaces:

ExponentialDistribution, QuasiFamily

public class Poisson
extends Poisson
implements QuasiFamily

The quasi Poisson family of GLM.

The R equivalent function is quasipoisson.

Constructor Summary

Poisson()
Create an instance of Poisson.

Poisson(LinkFunction link)
Create an instance of Poisson 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.Poisson

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

Poisson

public Poisson()

Create an instance of Poisson. The canonical link is Log.

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."

Poisson

public Poisson(LinkFunction link)

Create an instance of Poisson 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