SSJ
V. 1.2.5.

umontreal.iro.lecuyer.probdist
Class InverseGaussianDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by 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)1/2/(2πx3)exp-λ(x-μ)2/(2μ2x),         for x > 0.

The distribution function is given by

F(x) = Φ((λx)1/2($\displaystyle {\frac{{x}}{{\mu}}}$ -1)) + exp$\scriptstyle {\frac{{2\lambda}}{{\mu}}}$Φ(- (λx)1/2([tex2html_wrap_indisplay352] + 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
InverseGaussianDist(double mu, double lambda)
          Constructs the inverse Gaussian distribution with parameters μ and λ.
 
Method Summary
 double barF(double x)
          Returns bar(F)(x) = 1 - F(x).
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)
          Computes and 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 of X 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 in table x[i], i = 0, 1,…, n - 1.
 double getLambda()
          Returns the parameter λ of this object.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Estimates and returns the parameters [hat(μ), hat(λ)] of the inverse gaussian distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.
 double getMean()
          Returns the mean of the distribution function.
static double getMean(double mu, double lambda)
          Returns the mean E[X] = μ of the inverse gaussian distribution with parameters μ and λ.
 double getMu()
          Returns the parameter μ of this object.
 double getStandardDeviation()
          Returns the standard deviation of the distribution function.
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 of the distribution function.
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.
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.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
inverseBisection, inverseBrent, inverseF
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, 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 of X 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
Computes and 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 interface: Distribution
Returns 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

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


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.


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 in table 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

getMaximumLikelihoodEstimate

public static double[] getMaximumLikelihoodEstimate(double[] x,
                                                    int n)
Estimates and returns the parameters [hat(μ), hat(λ)] of the inverse gaussian distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.

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)]

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.


SSJ
V. 1.2.5.

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