HalfNormalDist (Java Libraries for Stochastic Simulation)

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

Constructors
Constructor and Description

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

Constructors
Constructor and Description
`HalfNormalDist(double mu, double sigma)` Constructs a `HalfNormalDist` object with parameters μ = `mu` and σ = `sigma`.

Method Summary

Methods
Modifier and Type	Method and Description
`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.
`java.lang.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 java.lang.String toString()
```
    Returns a String containing information about the current distribution.
    
    Overrides:
    
    toString in class java.lang.Object
    
    Returns:
    returns a String containing information about the current distribution.

Class HalfNormalDist

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

HalfNormalDist

Method Detail

density

cdf

barF

inverseF

getMean

getVariance

getStandardDeviation

density

cdf

barF

inverseF

getMLE

getMLE

getMean

getVariance

getStandardDeviation

getMu

getSigma

setParams

getParams

toString