SSJ
V. 1.2.5.

umontreal.iro.lecuyer.probdist
Class HyperbolicSecantDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.HyperbolicSecantDist
All Implemented Interfaces:
Distribution

public class HyperbolicSecantDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Hyperbolic Secant distribution with location parameter μ and scale parameter σ > 0. Its density is

f (x) = 1/(2σ) sech(π/2(x - μ)/σ)

The distribution function is given by

F(x) = 2/πtan-1[exp(π/2(x - μ)/σ)]

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
HyperbolicSecantDist(double mu, double sigma)
          Constructs a hyperbolic secant distribution with parameters μ and σ.
 
Method Summary
 double barF(double x)
          Returns bar(F)(x) = 1 - F(x).
static double barF(double mu, double sigma, double x)
          Computes the complementary distribution function of the hyperbolic secant distribution with parameters μ and σ.
 double cdf(double x)
          Computes and returns the distribution function F(x).
static double cdf(double mu, double sigma, double x)
          Computes the distribution function of the hyperbolic secant distribution with parameters μ and σ.
 double density(double x)
          Returns f (x), the density of X evaluated at x.
static double density(double mu, double sigma, double x)
          Computes the density function for a hyperbolic secant distribution with parameters μ and σ.
static HyperbolicSecantDist getInstanceFromMLE(double[] x, int n)
          Creates a new instance of a hyperbolic secant distribution with parameters μ and σ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Estimates and returns the parameters [hat(μ), hat(σ)] of the hyperbolic secant 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 sigma)
          Computes and returns the mean E[X] = μ of the hyperbolic secant distribution with parameters μ and σ.
 double getMu()
          Returns the parameter μ of this object.
 double getSigma()
          Returns the parameter σ of this object.
 double getStandardDeviation()
          Returns the standard deviation of the distribution function.
static double getStandardDeviation(double mu, double sigma)
          Computes and returns the standard deviation of the hyperbolic secant distribution with parameters μ and σ.
 double getVariance()
          Returns the variance of the distribution function.
static double getVariance(double mu, double sigma)
          Computes and returns the variance Var[X] = σ2 of the hyperbolic secant distribution with parameters μ and σ.
 double inverseF(double u)
          Computes and returns the inverse distribution function F-1(u), defined in.
static double inverseF(double mu, double sigma, double u)
          Computes the inverse of the hyperbolic secant distribution with parameters μ and σ.
 void setParams(double mu, double sigma)
          Sets the parameters μ and σ of this object.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
inverseBisection, inverseBrent
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

HyperbolicSecantDist

public HyperbolicSecantDist(double mu,
                            double sigma)
Constructs a hyperbolic secant distribution with parameters μ and σ.

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

inverseF

public double inverseF(double u)
Description copied from interface: Distribution
Computes and returns the inverse distribution function F-1(u), defined in.

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value in the interval (0, 1) for which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

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 sigma,
                             double x)
Computes the density function for a hyperbolic secant distribution with parameters μ and σ.


cdf

public static double cdf(double mu,
                         double sigma,
                         double x)
Computes the distribution function of the hyperbolic secant distribution with parameters μ and σ.


barF

public static double barF(double mu,
                          double sigma,
                          double x)
Computes the complementary distribution function of the hyperbolic secant distribution with parameters μ and σ.


inverseF

public static double inverseF(double mu,
                              double sigma,
                              double u)
Computes the inverse of the hyperbolic secant distribution with parameters μ and σ.


getInstanceFromMLE

public static HyperbolicSecantDist getInstanceFromMLE(double[] x,
                                                      int n)
Creates a new instance of a hyperbolic secant distribution with parameters μ and σ 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(σ)] of the hyperbolic secant 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 to use to evaluate parameters
n - the number of observations to use to evaluate parameters
Returns:
returns the parameters [hat(μ), hat(σ)]

getMean

public static double getMean(double mu,
                             double sigma)
Computes and returns the mean E[X] = μ of the hyperbolic secant distribution with parameters μ and σ.

Returns:
the mean of the hyperbolic secant distribution E[X] = μ

getVariance

public static double getVariance(double mu,
                                 double sigma)
Computes and returns the variance Var[X] = σ2 of the hyperbolic secant distribution with parameters μ and σ.

Returns:
the variance of the hyperbolic secant distribution Var[X] = σ2

getStandardDeviation

public static double getStandardDeviation(double mu,
                                          double sigma)
Computes and returns the standard deviation of the hyperbolic secant distribution with parameters μ and σ.

Returns:
the standard deviation of the hyperbolic secant distribution

getMu

public double getMu()
Returns the parameter μ of this object.


getSigma

public double getSigma()
Returns the parameter σ of this object.


setParams

public void setParams(double mu,
                      double sigma)
Sets the parameters μ and σ of this object.


SSJ
V. 1.2.5.

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