Package jline.api.mc

Class Ctmc_foxglynn

java.lang.Object

jline.api.mc.Ctmc_foxglynn

public final class Ctmc_foxglynn
extends Object

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final class	Ctmc_foxglynn.FoxGlynnWeights	Poisson weights on the Fox-Glynn truncation window.

Method Summary

Modifier and Type	Method	Description
static Matrix	ctmc_foxglynn(Matrix pi0, Matrix Q, double t)	Return the transient probability distribution of the CTMC by Fox-Glynn uniformization.
static Matrix	ctmc_foxglynn(Matrix pi0, Matrix Q, double t, double tol, int maxiter)	Return the transient probability distribution of the CTMC by Fox-Glynn uniformization.
static Ctmc_foxglynn.FoxGlynnWeights	ctmc_foxglynn_weights(double lambda, double tol, int maxiter)	Return the Fox-Glynn truncation window and normalized Poisson weights for a Poisson(lambda) mixing distribution at tail-mass tolerance tol.
static Ctmc_foxglynn.FoxGlynnWeights	ctmc_foxglynn_weights(double lambda, double tol, int maxiter, boolean normalize)	Return the Fox-Glynn truncation window and Poisson weights for a Poisson(lambda) mixing distribution at tail-mass tolerance tol.

Methods inherited from class java.lang.Object

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

Method Details

ctmc_foxglynn

public static Matrix ctmc_foxglynn(Matrix pi0,
 Matrix Q,
 double t)

Return the transient probability distribution of the CTMC by Fox-Glynn uniformization.

Parameters:

pi0 - Initial state of the CTMC

Q - Infinitesimal generator of the CTMC

t - Transient analysis period boundary [0,t]

Returns:

Transient probability vector at time t

ctmc_foxglynn

public static Matrix ctmc_foxglynn(Matrix pi0,
 Matrix Q,
 double t,
 double tol,
 int maxiter)

Return the transient probability distribution of the CTMC by Fox-Glynn uniformization.

Parameters:

pi0 - Initial state of the CTMC

Q - Infinitesimal generator of the CTMC

t - Transient analysis period boundary [0,t]

tol - Poisson tail-mass truncation tolerance

maxiter - Maximum truncation depth; pass a nonpositive value to let the Fox-Glynn right truncation point size it

Returns:

Transient probability vector at time t

ctmc_foxglynn_weights

public static Ctmc_foxglynn.FoxGlynnWeights ctmc_foxglynn_weights(double lambda,
 double tol,
 int maxiter)

Return the Fox-Glynn truncation window and normalized Poisson weights for a Poisson(lambda) mixing distribution at tail-mass tolerance tol.

Parameters:

lambda - Poisson rate, that is the uniformization constant times the horizon

tol - Poisson tail-mass truncation tolerance

maxiter - Cap on the right truncation point; nonpositive to leave it uncapped

Returns:

Truncation points and weights

ctmc_foxglynn_weights

public static Ctmc_foxglynn.FoxGlynnWeights ctmc_foxglynn_weights(double lambda,
 double tol,
 int maxiter,
 boolean normalize)

Return the Fox-Glynn truncation window and Poisson weights for a Poisson(lambda) mixing distribution at tail-mass tolerance tol.

With normalize set the window is rescaled to sum to one, as Fox and Glynn prescribe, so the truncated tails are redistributed over the window. Cleared, the anchor is scaled by the true mode probability through a log-gamma instead, so the returned values are the Poisson probabilities themselves and 1 - sum(w) is the discarded tail rather than being absorbed; Ctmc_fau needs that, its error being reported as missing mass rather than as a bound.

Parameters:

lambda - Poisson rate, that is the uniformization constant times the horizon

tol - Poisson tail-mass truncation tolerance

maxiter - Cap on the right truncation point; nonpositive to leave it uncapped

normalize - Rescale the window to sum to one, rather than returning the true Poisson probabilities

Returns:

Truncation points and weights