umontreal.iro.lecuyer.stochprocess

Class InverseGaussianProcess

java.lang.Object

umontreal.iro.lecuyer.stochprocess.StochasticProcess

umontreal.iro.lecuyer.stochprocess.InverseGaussianProcess

Direct Known Subclasses:

InverseGaussianProcessMSH, InverseGaussianProcessPCA

public class InverseGaussianProcess
extends StochasticProcess

The inverse Gaussian process is a non-decreasing process where the increments are additive and are given by the inverse gaussian distribution, InverseGaussianDist. With parameters δ and γ, the time increments are given by InverseGaussianDist (δdt/γ, δ²dt²).

[We here use the inverse gaussian distribution parametrized with IGDist (μ, λ), where μ = δ/γ and λ = δ². If we instead used the parametrization IGDist(δ, γ), then the increment distribution of our process would have been written more simply as IGDist^{[tex2html_wrap_inline158]}(δdt, γ).]

The increments are generated by using the inversion of the cumulative distribution function. It therefore uses only one RandomStream. Subclasses of this class use different generating methods and some need two RandomStream's.

The initial value of this process is the initial observation time.

Constructor Summary

Constructors

Constructor and Description
InverseGaussianProcess(double s0, double delta, double gamma, RandomStream stream) Constructs a new InverseGaussianProcess.

Method Summary

Modifier and Type	Method and Description
double[]	generatePath() Generates, returns, and saves the sample path {X(t0), X(t1),…, X(td)}.
double[]	generatePath(double[] uniforms01) Instead of using the internal stream to generate the path, uses an array of uniforms U[0, 1).
double[]	generatePath(double[] uniforms01, double[] uniforms01b) This method does not work for this class, but will be useful for the subclasses that require two streams.
double	getAnalyticAverage(double time) Returns the analytic average which is δt/γ, with t = time.
double	getAnalyticVariance(double time) Returns the analytic variance which is (δt)2, with t = time.
double	getDelta() Returns δ.
double	getGamma() Returns γ.
int	getNumberOfRandomStreams() Returns the number of random streams of this process.
RandomStream	getStream() Returns the random stream of the underlying generator.
double	nextObservation() Generates and returns the next observation X(tj) of the stochastic process.
void	setParams(double delta, double gamma) Sets the parameters.
void	setStream(RandomStream stream) Resets the random stream of the underlying generator to stream.

Methods inherited from class umontreal.iro.lecuyer.stochprocess.StochasticProcess

generatePath, getArrayMappingCounterToIndex, getCurrentObservation, getCurrentObservationIndex, getNbObservationTimes, getObservation, getObservationTimes, getPath, getSubpath, getX0, hasNextObservation, resetStartProcess, setObservationTimes, setObservationTimes, setX0

Methods inherited from class java.lang.Object

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

Constructor Detail

InverseGaussianProcess

public InverseGaussianProcess(double s0,
                              double delta,
                              double gamma,
                              RandomStream stream)

Constructs a new InverseGaussianProcess. The initial value s0 will be overridden by t[0] when the observation times are set.

Method Detail

generatePath

public double[] generatePath()

Description copied from class: StochasticProcess

Generates, returns, and saves the sample path {X(t₀), X(t₁),…, X(t_d)}. It can then be accessed via getPath, getSubpath, or getObservation. The generation method depends on the process type.

Specified by:

generatePath in class StochasticProcess

generatePath

public double[] generatePath(double[] uniforms01)

Instead of using the internal stream to generate the path, uses an array of uniforms U[0, 1). The array should be of the length of the number of periods in the observation times. This method is useful for NormalInverseGaussianProcess.

generatePath

public double[] generatePath(double[] uniforms01,
                             double[] uniforms01b)

This method does not work for this class, but will be useful for the subclasses that require two streams.

nextObservation

public double nextObservation()

Description copied from class: StochasticProcess

Generates and returns the next observation X(t_j) of the stochastic process. The processes are usually sampled sequentially, i.e. if the last observation generated was for time t_j-1, the next observation returned will be for time t_j. In some cases, subclasses extending this abstract class may use non-sequential sampling algorithms (such as bridge sampling). The order of generation of the t_j's is then specified by the subclass. All the processes generated using principal components analysis (PCA) do not have this method.

Overrides:

nextObservation in class StochasticProcess

setParams

public void setParams(double delta,
                      double gamma)

Sets the parameters.

getDelta

public double getDelta()

Returns δ.

getGamma

public double getGamma()

Returns γ.

getAnalyticAverage

public double getAnalyticAverage(double time)

Returns the analytic average which is δt/γ, with t = time.

getAnalyticVariance

public double getAnalyticVariance(double time)

Returns the analytic variance which is (δt)², with t = time.

getStream

public RandomStream getStream()

Description copied from class: StochasticProcess

Returns the random stream of the underlying generator.

Specified by:

getStream in class StochasticProcess

setStream

public void setStream(RandomStream stream)

Description copied from class: StochasticProcess

Resets the random stream of the underlying generator to stream.

Specified by:

setStream in class StochasticProcess

getNumberOfRandomStreams

public int getNumberOfRandomStreams()

Returns the number of random streams of this process. It is useful because some subclasses use different number of streams. It returns 1 for InverseGaussianProcess.