SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist Class FoldedNormalDist

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

`public class FoldedNormalDistextends ContinuousDistribution`

Extends the class `ContinuousDistribution` for the folded normal distribution with parameters μ >=  0 and σ > 0. The density is

f (x) = φ((x - μ)/σ) + φ((- x - μ)/σ)        for x >= 0,

f (x) = 0,         for x < 0,

where φ denotes the density function of a standard normal distribution.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`decPrec`

Constructor Summary
```FoldedNormalDist(double mu, double sigma)```
Constructs a FoldedNormalDist 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 folded normal distribution.
` double` `getMean()`
Returns the mean.
`static double` ```getMean(double mu, double sigma)```
.
`static double[]` ```getMLE(double[] x, int n)```
NOT IMPLEMENTED.
` 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 folded normal distribution with parameters μ and σ.
` double` `getVariance()`
Returns the variance.
`static double` ```getVariance(double mu, double sigma)```
.
` 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 for this object.
` 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

FoldedNormalDist

```public FoldedNormalDist(double mu,
double sigma)```
Constructs a FoldedNormalDist 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 folded 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

getMean

```public static double getMean(double mu,
double sigma)```
. Computes and returns the mean

E[X] = σ()1/22π  e-μ2/(2σ2) + μ erf(1#1),

where erf(z) is the error function.

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] = μ2 + σ2 - E[X]2.

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 folded normal distribution with parameters μ and σ.

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

getMLE

```public static double[] getMLE(double[] x,
int n)```
NOT IMPLEMENTED. Les formules pour le MLE sont données dans.

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(σ)]

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 for this object.

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.