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

Class Gaussian

java.lang.Object

com.numericalmethod.suanshu.stats.regression.linear.glm.distribution.Family

com.numericalmethod.suanshu.stats.regression.linear.glm.distribution.Gaussian

com.numericalmethod.suanshu.stats.regression.linear.glm.quasi.family.Gaussian

All Implemented Interfaces:

ExponentialDistribution, QuasiFamily, java.io.Serializable

public class Gaussian
extends Gaussian
implements QuasiFamily

The quasi Gaussian family of GLM.

The R equivalent function is quasi.

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
Gaussian() Create an instance of Gaussian.
Gaussian(LinkFunction link) Create an instance of Gaussian 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.Gaussian

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

Gaussian

public Gaussian()

Create an instance of Gaussian. The canonical link is Identity.

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."

Gaussian

public Gaussian(LinkFunction link)

Create an instance of Gaussian 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