SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist Class HalfNormalDist

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

`public class HalfNormalDistextends 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.