InverseGaussianDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdist.ContinuousDistribution
- - umontreal.iro.lecuyer.probdist.InverseGaussianDist

All Implemented Interfaces:

Distribution
```
public class InverseGaussianDist
extends ContinuousDistribution
```
Extends the class ContinuousDistribution for the inverse Gaussian distribution with location parameter μ > 0 and scale parameter λ > 0. Its density is

f (x) = (λ/ (2πx^3))^1/2e^{-λ(x-μ)²/(2μ²x)}, for x > 0.
The distribution function is given by

F(x) = Φ((λ/x)^1/2(x/μ -1)) + e^2λ/μΦ(- (λ/x)^1/2(x/μ + 1)),
where Φ is the standard normal distribution function.
The non-static versions of the methods cdf, barF, and inverseF call the static version of the same name.

Field Summary
- Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
  decPrec

Constructor Summary

Constructors
Constructor and Description

InverseGaussianDist(double mu, double lambda)
Constructs the inverse Gaussian distribution with parameters μ and λ.

Constructors
Constructor and Description
`InverseGaussianDist(double mu, double lambda)` Constructs the inverse Gaussian distribution with parameters μ and λ.

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`barF(double x)` Returns the complementary distribution function.
`static double`	`barF(double mu, double lambda, double x)` Computes the complementary distribution function of the inverse gaussian distribution with parameters μ and λ, evaluated at x.
`double`	`cdf(double x)` Returns the distribution function F(x).
`static double`	`cdf(double mu, double lambda, double x)` Computes the distribution function of the inverse gaussian distribution with parameters μ and λ, evaluated at x.
`double`	`density(double x)` Returns f (x), the density evaluated at x.
`static double`	`density(double mu, double lambda, double x)` Computes the density function for the inverse gaussian distribution with parameters μ and λ, evaluated at x.
`static InverseGaussianDist`	`getInstanceFromMLE(double[] x, int n)` Creates a new instance of an inverse gaussian distribution with parameters μ and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
`double`	`getLambda()` Returns the parameter λ of this object.
`static double[]`	`getMaximumLikelihoodEstimate(double[] x, int n)` Deprecated.
`double`	`getMean()` Returns the mean.
`static double`	`getMean(double mu, double lambda)` Returns the mean E[X] = μ of the inverse gaussian distribution with parameters μ and λ.
`static double[]`	`getMLE(double[] x, int n)` Estimates the parameters (μ, λ) of the inverse gaussian distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
`double`	`getMu()` Returns the parameter μ of this object.
`double[]`	`getParams()` Return a table containing the parameters of the current distribution.
`double`	`getStandardDeviation()` Returns the standard deviation.
`static double`	`getStandardDeviation(double mu, double lambda)` Computes and returns the standard deviation of the inverse gaussian distribution with parameters μ and λ.
`double`	`getVariance()` Returns the variance.
`static double`	`getVariance(double mu, double lambda)` Computes and returns the variance Var[X] = μ³/λ of the inverse gaussian distribution with parameters μ and λ.
`double`	`inverseF(double u)` Returns the inverse distribution function x = F^-1(u).
`static double`	`inverseF(double mu, double lambda, double u)` Computes the inverse of the inverse gaussian distribution with parameters μ and λ.
`void`	`setParams(double mu, double lambda)` Sets the parameters μ and λ of this object.
`java.lang.String`	`toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - InverseGaussianDist
```
public InverseGaussianDist(double mu,
                   double lambda)
```
    Constructs the inverse Gaussian distribution with parameters μ and λ.
- Method Detail
  - density
```
public double density(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns f (x), the density evaluated at x.
    
    Specified by:
    
    density in class ContinuousDistribution
    
    Parameters:
    x - value at which the density is evaluated
    
    Returns:
    density function evaluated at x
  - cdf
```
public double cdf(double x)
```
    Description copied from interface: Distribution
    
    Returns the distribution function F(x).
    
    Parameters:
    x - value at which the distribution function is evaluated
    
    Returns:
    distribution function evaluated at x
  - barF
```
public double barF(double x)
```
    Description copied from class: ContinuousDistribution
    
    Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).
    
    Specified by:
    
    barF in interface Distribution
    
    Overrides:
    
    barF in class ContinuousDistribution
    
    Parameters:
    x - value at which the complementary distribution function is evaluated
    
    Returns:
    complementary distribution function evaluated at x
  - inverseF
```
public double inverseF(double u)
```
    Description copied from class: ContinuousDistribution
    
    Returns the inverse distribution function x = F^-1(u). Restrictions: u∈[0, 1].
    
    Specified by:
    
    inverseF in interface Distribution
    
    Overrides:
    
    inverseF in class ContinuousDistribution
    
    Parameters:
    u - value at which the inverse distribution function is evaluated
    
    Returns:
    the inverse distribution function evaluated at u
  - getMean
```
public double getMean()
```
    Description copied from class: ContinuousDistribution
    
    Returns the mean.
    
    Specified by:
    
    getMean in interface Distribution
    
    Overrides:
    
    getMean in class ContinuousDistribution
    
    Returns:
    the mean
  - getVariance
```
public double getVariance()
```
    Description copied from class: ContinuousDistribution
    
    Returns the variance.
    
    Specified by:
    
    getVariance in interface Distribution
    
    Overrides:
    
    getVariance in class ContinuousDistribution
    
    Returns:
    the variance
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Description copied from class: ContinuousDistribution
    
    Returns the standard deviation.
    
    Specified by:
    
    getStandardDeviation in interface Distribution
    
    Overrides:
    
    getStandardDeviation in class ContinuousDistribution
    
    Returns:
    the standard deviation
  - density
```
public static double density(double mu,
             double lambda,
             double x)
```
    Computes the density function for the inverse gaussian distribution with parameters μ and λ, evaluated at x.
  - cdf
```
public static double cdf(double mu,
         double lambda,
         double x)
```
    Computes the distribution function of the inverse gaussian distribution with parameters μ and λ, evaluated at x.
  - barF
```
public static double barF(double mu,
          double lambda,
          double x)
```
    Computes the complementary distribution function of the inverse gaussian distribution with parameters μ and λ, evaluated at x.
  - inverseF
```
public static double inverseF(double mu,
              double lambda,
              double u)
```
    Computes the inverse of the inverse gaussian distribution with parameters μ and λ.
  - getMLE
```
public static double[] getMLE(double[] x,
              int n)
```
    Estimates the parameters (μ, λ) of the inverse gaussian distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [μ, λ].
    
    Parameters:
    x - the list of observations used to evaluate parameters
    n - the number of observations used to evaluate parameters
    
    Returns:
    returns the parameters [hat(μ), hat(λ)]
  - getMaximumLikelihoodEstimate
```
@Deprecated
public static double[] getMaximumLikelihoodEstimate(double[] x,
                                               int n)
```
    Deprecated.
    
    Same as getMLE.
  - getInstanceFromMLE
```
public static InverseGaussianDist getInstanceFromMLE(double[] x,
                                     int n)
```
    Creates a new instance of an inverse gaussian distribution with parameters μ and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
    
    Parameters:
    x - the list of observations to use to evaluate parameters
    n - the number of observations to use to evaluate parameters
  - getMean
```
public static double getMean(double mu,
             double lambda)
```
    Returns the mean E[X] = μ of the inverse gaussian distribution with parameters μ and λ.
    
    Returns:
    the mean of the inverse gaussian distribution E[X] = μ
  - getVariance
```
public static double getVariance(double mu,
                 double lambda)
```
    Computes and returns the variance Var[X] = μ³/λ of the inverse gaussian distribution with parameters μ and λ.
    
    Returns:
    the variance of the inverse gaussian distribution Var[X] = μ³/λ
  - getStandardDeviation
```
public static double getStandardDeviation(double mu,
                          double lambda)
```
    Computes and returns the standard deviation of the inverse gaussian distribution with parameters μ and λ.
    
    Returns:
    the standard deviation of the inverse gaussian distribution
  - getLambda
```
public double getLambda()
```
    Returns the parameter λ of this object.
  - getMu
```
public double getMu()
```
    Returns the parameter μ of this object.
  - setParams
```
public void setParams(double mu,
             double lambda)
```
    Sets the parameters μ and λ of this object.
  - getParams
```
public double[] getParams()
```
    Return a table containing the parameters of the current distribution. This table is put in regular order: [μ, λ].
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class InverseGaussianDist

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Constructor Summary

Method Summary

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

Methods inherited from class java.lang.Object

Constructor Detail

InverseGaussianDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMLE

getMaximumLikelihoodEstimate

getInstanceFromMLE

getMean

getVariance

getStandardDeviation

getLambda

getMu

setParams

getParams

toString