SSJ
V. 2.6.

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 InverseGaussianProcessextends 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 IGDist1#1(δ, γ), then the increment distribution of our process would have been written more simply as IGDist[tex2html_wrap_inline160](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
```InverseGaussianProcess(double s0, double delta, double gamma, RandomStream stream)```
Constructs a new InverseGaussianProcess.

Method Summary
` 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(td)}. 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(tj) of the stochastic process. The processes are usually sampled sequentially, i.e. if the last observation generated was for time tj-1, the next observation returned will be for time tj. In some cases, subclasses extending this abstract class may use non-sequential sampling algorithms (such as bridge sampling). The order of generation of the tj'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`.

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.