SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class HalfNormalDist

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

public class HalfNormalDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the half-normal distribution with parameters μ and σ > 0. Its density is

f (x) = ((2/π)1/2/σ)e-(x-μ)2/(2σ2),        for x > = μ,

f (x) = 0        for x < μ,


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
HalfNormalDist(double mu, double sigma)
          Constructs a HalfNormalDist object with parameters μ = mu and σ = sigma.
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double mu, double sigma, double x)
          Computes the complementary distribution function.
 double cdf(double x)
          Returns the distribution function F(x).
static double cdf(double mu, double sigma, double x)
          Computes the distribution function.
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double mu, double sigma, double x)
          Computes the density function of the half-normal distribution.
 double getMean()
          Returns the mean.
static double getMean(double mu, double sigma)
          Computes and returns the mean E[X] = μ + σ(2 / π)1/2.
static double[] getMLE(double[] x, int n)
          Estimates the parameters μ and σ of the half-normal distribution using the maximum likelihood method from the n observations x[i], i = 0, 1,…, n - 1.
static double[] getMLE(double[] x, int n, double mu)
          Estimates the parameter σ of the half-normal distribution using the maximum likelihood method from the n observations x[i], i = 0, 1,…, n - 1 and the parameter μ = mu.
 double getMu()
          Returns the parameter μ of this object.
 double[] getParams()
          Return a table containing the parameters of the current distribution.
 double getSigma()
          Returns the parameter σ of this object.
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double mu, double sigma)
          Computes the standard deviation of the half-normal distribution with parameters μ and σ.
 double getVariance()
          Returns the variance.
static double getVariance(double mu, double sigma)
          Computes and returns the variance Var[X] = (1 - 2/π)σ2.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double mu, double sigma, double u)
          Computes the inverse of the distribution function.
 void setParams(double mu, double sigma)
          Sets the parameters μ and σ.
 String toString()
          Returns a String containing information about the current distribution.
 
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

HalfNormalDist

public HalfNormalDist(double mu,
                      double sigma)
Constructs a HalfNormalDist object with parameters μ = mu and σ = sigma.

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 sigma,
                             double x)
Computes the density function of the half-normal distribution.

Parameters:
mu - the parameter mu
sigma - the parameter sigma
x - the value at which the density is evaluated
Returns:
returns the density function

cdf

public static double cdf(double mu,
                         double sigma,
                         double x)
Computes the distribution function.

Parameters:
mu - the parameter mu
sigma - the parameter sigma
x - the value at which the distribution is evaluated
Returns:
returns the cdf function

barF

public static double barF(double mu,
                          double sigma,
                          double x)
Computes the complementary distribution function.

Parameters:
mu - the parameter mu
sigma - the parameter sigma
x - the value at which the complementary distribution is evaluated
Returns:
returns the complementary distribution function

inverseF

public static double inverseF(double mu,
                              double sigma,
                              double u)
Computes the inverse of the distribution function.

Parameters:
mu - the parameter mu
sigma - the parameter sigma
u - the value at which the inverse distribution is evaluated
Returns:
returns the inverse distribution function

getMLE

public static double[] getMLE(double[] x,
                              int n)
Estimates the parameters μ and σ of the half-normal 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: [μ, σ].

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 [μ, σ]

getMLE

public static double[] getMLE(double[] x,
                              int n,
                              double mu)
Estimates the parameter σ of the half-normal distribution using the maximum likelihood method from the n observations x[i], i = 0, 1,…, n - 1 and the parameter μ = mu. The estimate is returned in a one-element array: [σ].

Parameters:
x - the list of observations to use to evaluate parameters
n - the number of observations to use to evaluate parameter
mu - the parameter mu
Returns:
returns the parameter [σ]

getMean

public static double getMean(double mu,
                             double sigma)
Computes and returns the mean E[X] = μ + σ(2 / π)1/2.

Parameters:
mu - the parameter mu
sigma - the parameter sigma
Returns:
returns the mean

getVariance

public static double getVariance(double mu,
                                 double sigma)
Computes and returns the variance Var[X] = (1 - 2/π)σ2.

Parameters:
mu - the parameter mu
sigma - the parameter sigma
Returns:
returns the variance

getStandardDeviation

public static double getStandardDeviation(double mu,
                                          double sigma)
Computes the standard deviation of the half-normal distribution with parameters μ and σ.

Parameters:
mu - the parameter mu
sigma - the parameter sigma
Returns:
returns the standard deviation

getMu

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

Returns:
returns the parameter mu

getSigma

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

Returns:
returns the parameter sigma

setParams

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

Parameters:
mu - the parameter mu
sigma - the parameter sigma

getParams

public double[] getParams()
Return a table containing the parameters of the current distribution. This table is put in regular order: [μ, σ].

Returns:
returns the parameters [μ, σ]

toString

public String toString()
Returns a String containing information about the current distribution.

Overrides:
toString in class Object
Returns:
returns a String containing information about the current distribution.

SSJ
V. 2.6.

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