SSJ  3.3.1
Stochastic Simulation in Java
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FoldedNormalDist Class Reference

Extends the class ContinuousDistribution for the folded normal distribution with parameters \(\mu\ge0\) and \(\sigma> 0\). More...

Inheritance diagram for FoldedNormalDist:
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Collaboration diagram for FoldedNormalDist:
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Public Member Functions

 FoldedNormalDist (double mu, double sigma)
 Constructs a FoldedNormalDist object with parameters \(\mu=\) mu and \(\sigma=\) sigma.
 
double density (double x)
 
double cdf (double x)
 Returns the distribution function \(F(x)\). More...
 
double barF (double x)
 Returns \(\bar{F}(x) = 1 - F(x)\). More...
 
double inverseF (double u)
 Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ). More...
 
double getMean ()
 Returns the mean of the distribution function.
 
double getVariance ()
 Returns the variance of the distribution function.
 
double getStandardDeviation ()
 Returns the standard deviation of the distribution function.
 
double getMu ()
 Returns the parameter \(\mu\) of this object. More...
 
double getSigma ()
 Returns the parameter \(\sigma\) of this object. More...
 
void setParams (double mu, double sigma)
 Sets the parameters \(\mu\) and \(\sigma\) for this object. More...
 
double [] getParams ()
 Return a table containing the parameters of the current distribution. More...
 
String toString ()
 Returns a String containing information about the current distribution. More...
 
- Public Member Functions inherited from ContinuousDistribution
abstract double density (double x)
 Returns \(f(x)\), the density evaluated at \(x\). More...
 
double barF (double x)
 Returns the complementary distribution function. More...
 
double inverseBrent (double a, double b, double u, double tol)
 Computes the inverse distribution function \(x = F^{-1}(u)\), using the Brent-Dekker method. More...
 
double inverseBisection (double u)
 Computes and returns the inverse distribution function \(x = F^{-1}(u)\), using bisection. More...
 
double inverseF (double u)
 Returns the inverse distribution function \(x = F^{-1}(u)\). More...
 
double getMean ()
 Returns the mean. More...
 
double getVariance ()
 Returns the variance. More...
 
double getStandardDeviation ()
 Returns the standard deviation. More...
 
double getXinf ()
 Returns \(x_a\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
double getXsup ()
 Returns \(x_b\) such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXinf (double xa)
 Sets the value \(x_a=\) xa, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 
void setXsup (double xb)
 Sets the value \(x_b=\) xb, such that the probability density is 0 everywhere outside the interval \([x_a, x_b]\). More...
 

Static Public Member Functions

static double density (double mu, double sigma, double x)
 Computes the density function of the folded normal distribution. More...
 
static double cdf (double mu, double sigma, double x)
 Computes the distribution function. More...
 
static double barF (double mu, double sigma, double x)
 Computes the complementary distribution function. More...
 
static double inverseF (double mu, double sigma, double u)
 Computes the inverse of the distribution function. More...
 
static double getMean (double mu, double sigma)
 Computes and returns the mean

\[ E[X] = \sigma\sqrt{\frac{2}{\pi}}\; e^{-\mu^2/(2\sigma^2)} + \mu \mbox{erf}\left(\frac{\mu}{\sigma\sqrt{2}}\right), \]

where erf \((z)\) is the error function. More...

 
static double getVariance (double mu, double sigma)
 Computes and returns the variance

\[ \mbox{Var}[X] = \mu^2 + \sigma^2 - E[X]^2. \]

. More...

 
static double getStandardDeviation (double mu, double sigma)
 Computes the standard deviation of the folded normal distribution with parameters \(\mu\) and \(\sigma\). More...
 
static double [] getMLE (double[] x, int n)
 NOT IMPLEMENTED. More...
 

Protected Attributes

double mu
 
double sigma
 
- Protected Attributes inherited from ContinuousDistribution
double supportA = Double.NEGATIVE_INFINITY
 
double supportB = Double.POSITIVE_INFINITY
 

Additional Inherited Members

- Public Attributes inherited from ContinuousDistribution
int decPrec = 15
 
- Static Protected Attributes inherited from ContinuousDistribution
static final double XBIG = 100.0
 
static final double XBIGM = 1000.0
 
static final double [] EPSARRAY
 

Detailed Description

Extends the class ContinuousDistribution for the folded normal distribution with parameters \(\mu\ge0\) and \(\sigma> 0\).

The density is

\[ f(x) = \phi\left(\frac{x-\mu}{\sigma}\right) + \phi\left(\frac{-x-\mu}{\sigma}\right) \qquad\mbox{for } x \ge0, \tag{fFoldedNormal} \]

\[ f(x) = 0, \qquad\mbox{ for } x < 0, \]

where \( \phi\) denotes the density function of a standard normal distribution.

Member Function Documentation

◆ barF() [1/2]

double barF ( double  x)

Returns \(\bar{F}(x) = 1 - F(x)\).

Parameters
xvalue at which the complementary distribution function is evaluated
Returns
complementary distribution function evaluated at x

Implements Distribution.

◆ barF() [2/2]

static double barF ( double  mu,
double  sigma,
double  x 
)
static

Computes the complementary distribution function.

Parameters
muthe parameter mu
sigmathe parameter sigma
xthe value at which the complementary distribution is evaluated
Returns
returns the complementary distribution function

◆ cdf() [1/2]

double cdf ( double  x)

Returns the distribution function \(F(x)\).

Parameters
xvalue at which the distribution function is evaluated
Returns
distribution function evaluated at x

Implements Distribution.

◆ cdf() [2/2]

static double cdf ( double  mu,
double  sigma,
double  x 
)
static

Computes the distribution function.

Parameters
muthe parameter mu
sigmathe parameter sigma
xthe value at which the distribution is evaluated
Returns
returns the cdf function

◆ density()

static double density ( double  mu,
double  sigma,
double  x 
)
static

Computes the density function of the folded normal distribution.

Parameters
muthe parameter mu
sigmathe parameter sigma
xthe value at which the density is evaluated
Returns
returns the density function

◆ getMean()

static double getMean ( double  mu,
double  sigma 
)
static

Computes and returns the mean

\[ E[X] = \sigma\sqrt{\frac{2}{\pi}}\; e^{-\mu^2/(2\sigma^2)} + \mu \mbox{erf}\left(\frac{\mu}{\sigma\sqrt{2}}\right), \]

where erf \((z)\) is the error function.

Parameters
muthe parameter mu
sigmathe parameter sigma
Returns
returns the mean

◆ getMLE()

static double [] getMLE ( double []  x,
int  n 
)
static

NOT IMPLEMENTED.

Les formules pour le MLE sont données dans [164] .

Parameters
xthe list of observations used to evaluate parameters
nthe number of observations used to evaluate parameters
Returns
returns the parameters [ \(\hat{\mu}\), \(\hat{\sigma}\)]

◆ getMu()

double getMu ( )

Returns the parameter \(\mu\) of this object.

Returns
returns the parameter mu

◆ getParams()

double [] getParams ( )

Return a table containing the parameters of the current distribution.

This table is put in regular order: [ \(\mu\), \(\sigma\)].

Returns
returns the parameters [ \(\mu\), \(\sigma\)]

Implements Distribution.

◆ getSigma()

double getSigma ( )

Returns the parameter \(\sigma\) of this object.

Returns
returns the parameter sigma

◆ getStandardDeviation()

static double getStandardDeviation ( double  mu,
double  sigma 
)
static

Computes the standard deviation of the folded normal distribution with parameters \(\mu\) and \(\sigma\).

Parameters
muthe parameter mu
sigmathe parameter sigma
Returns
returns the standard deviation

◆ getVariance()

static double getVariance ( double  mu,
double  sigma 
)
static

Computes and returns the variance

\[ \mbox{Var}[X] = \mu^2 + \sigma^2 - E[X]^2. \]

.

Parameters
muthe parameter mu
sigmathe parameter sigma
Returns
returns the variance

◆ inverseF() [1/2]

double inverseF ( double  u)

Returns the inverse distribution function \(F^{-1}(u)\), defined in ( inverseF ).

Parameters
uvalue in the interval \((0,1)\) for which the inverse distribution function is evaluated
Returns
the inverse distribution function evaluated at u

Implements Distribution.

◆ inverseF() [2/2]

static double inverseF ( double  mu,
double  sigma,
double  u 
)
static

Computes the inverse of the distribution function.

Parameters
muthe parameter mu
sigmathe parameter sigma
uthe value at which the inverse distribution is evaluated
Returns
returns the inverse distribution function

◆ setParams()

void setParams ( double  mu,
double  sigma 
)

Sets the parameters \(\mu\) and \(\sigma\) for this object.

Parameters
muthe parameter mu
sigmathe parameter sigma

◆ toString()

String toString ( )

Returns a String containing information about the current distribution.

Returns
returns a String containing information about the current distribution.

The documentation for this class was generated from the following file: