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, java.io.Serializable

public class Poisson
extends Poisson
implements QuasiFamily

The quasi Poisson family of GLM.

The R equivalent function is quasipoisson.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
Poisson() Create an instance of Poisson.
Poisson(LinkFunction link) Create an instance of Poisson with an overriding link function.

Method Summary

Modifier and Type	Method and Description
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)
Family	toFamily()

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."

toFamily

public Family toFamily()

Specified by:

toFamily in interface QuasiFamily