A variant of the class NormalDist (for the normal distribution with mean \(\mu\) and variance \(\sigma^2\)). More...

Inheritance diagram for umontreal.ssj.probdist.NormalDistQuick:

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

Static Public Member Functions
static double	cdf01 (double x)
	Same as `cdf(0.0, 1.0, x)`.
static double	cdf (double mu, double sigma, double x)
	Returns an approximation of \(\Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.
static double	barF01 (double x)
	Same as `barF(0.0, 1.0, x)`.
static double	barF (double mu, double sigma, double x)
	Returns an approximation of \(1 - \Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.
static double	inverseF01 (double u)
	Same as `inverseF(0.0, 1.0, u)`.
static double	inverseF (double mu, double sigma, double u)
	Returns an approximation of \(\Phi^{-1}(u)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.
Static Public Member Functions inherited from umontreal.ssj.probdist.NormalDist
static double	density01 (double x)
	Same as `density(0, 1, x)`.
static double	density (double mu, double sigma, double x)
	Computes the normal density function ( `fnormal` ).
static double[]	getMLE (double[] x, int n)
	Estimates the parameters \((\mu, \sigma)\) of the normal distribution using the maximum likelihood method, from the \(n\) observations \(x[i]\), \(i = 0, 1,…, n-1\).
static NormalDist	getInstanceFromMLE (double[] x, int n)
	Creates a new instance of a normal distribution with parameters.
static double	getMean (double mu, double sigma)
	Computes and returns the mean \(E[X] = \mu\) of the normal distribution with parameters \(\mu\) and \(\sigma\).
static double	getVariance (double mu, double sigma)
	Computes and returns the variance \(\mbox{Var}[X] = \sigma^2\) of the normal distribution with parameters \(\mu\) and.
static double	getStandardDeviation (double mu, double sigma)
	Computes and returns the standard deviation \(\sigma\) of the normal distribution with parameters \(\mu\) and \(\sigma\).

Detailed Description

A variant of the class NormalDist (for the normal distribution with mean \(\mu\) and variance \(\sigma^2\)).

The difference is in the implementation of the methods cdf01, barF01 and inverseF01, which are faster but less accurate than those of the class

NormalDist.

 <div class="SSJ-bigskip"></div>

Definition at line 26 of file NormalDistQuick.java.

Constructor & Destructor Documentation

◆ NormalDistQuick() [1/2]

umontreal.ssj.probdist.NormalDistQuick.NormalDistQuick ( )

Constructs a NormalDistQuick object with default parameters.

\(\mu= 0\) and \(\sigma= 1\).

Definition at line 33 of file NormalDistQuick.java.

◆ NormalDistQuick() [2/2]

umontreal.ssj.probdist.NormalDistQuick.NormalDistQuick	(	double	mu,
		double	sigma )

Constructs a NormalDistQuick object with mean \(\mu\) = mu and standard deviation \(\sigma\) = sigma.

Definition at line 41 of file NormalDistQuick.java.

Member Function Documentation

◆ barF() [1/2]

double umontreal.ssj.probdist.NormalDistQuick.barF	(	double	mu,
		double	sigma,
		double	x )

static

Returns an approximation of \(1 - \Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.

Uses Marsaglia et al’s [170] fast method with table lookups. Returns 15 decimal digits of precision. This method is approximately twice faster than NormalDist.barF.

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 165 of file NormalDistQuick.java.

◆ barF() [2/2]

double umontreal.ssj.probdist.NormalDistQuick.barF ( double x )

Returns the complementary distribution function.

The default implementation computes \(\bar{F}(x) = 1 - F(x)\).

Parameters

x	value at which the complementary distribution function is evaluated

Returns: complementary distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 56 of file NormalDistQuick.java.

◆ barF01()

double umontreal.ssj.probdist.NormalDistQuick.barF01 ( double x )

static

Same as barF(0.0, 1.0, x).

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 154 of file NormalDistQuick.java.

◆ cdf() [1/2]

double umontreal.ssj.probdist.NormalDistQuick.cdf	(	double	mu,
		double	sigma,
		double	x )

static

Returns an approximation of \(\Phi(x)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.

Uses Marsaglia et al’s [170] fast method with table lookups. Returns 15 decimal digits of precision. This method is approximately 60% faster than NormalDist.cdf.

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 145 of file NormalDistQuick.java.

◆ cdf() [2/2]

double umontreal.ssj.probdist.NormalDistQuick.cdf ( double x )

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

Parameters

x	value at which the distribution function is evaluated

Returns: distribution function evaluated at x

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 52 of file NormalDistQuick.java.

◆ cdf01()

double umontreal.ssj.probdist.NormalDistQuick.cdf01 ( double x )

static

Same as cdf(0.0, 1.0, x).

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 95 of file NormalDistQuick.java.

◆ inverseF() [1/2]

double umontreal.ssj.probdist.NormalDistQuick.inverseF	(	double	mu,
		double	sigma,
		double	u )

static

Returns an approximation of \(\Phi^{-1}(u)\), where \(\Phi\) is the standard normal distribution function, with mean 0 and variance 1.

Uses the method of Marsaglia, Zaman, and Marsaglia

[170] , with table lookups. Returns 6 decimal digits of precision. This method is approximately 20% faster than NormalDist.inverseF.

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 533 of file NormalDistQuick.java.

◆ inverseF() [2/2]

double umontreal.ssj.probdist.NormalDistQuick.inverseF ( double u )

Returns the inverse distribution function \(x = F^{-1}(u)\).

Restrictions: \(u \in[0,1]\).

Parameters

u	value at which the inverse distribution function is evaluated

Returns: the inverse distribution function evaluated at u

Exceptions

IllegalArgumentException if \(u\) is not in the interval \([0,1]\)

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 60 of file NormalDistQuick.java.

◆ inverseF01()

double umontreal.ssj.probdist.NormalDistQuick.inverseF01 ( double u )

static

Same as inverseF(0.0, 1.0, u).

Reimplemented from umontreal.ssj.probdist.NormalDist.

Definition at line 476 of file NormalDistQuick.java.

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

src/main/java/umontreal/ssj/probdist/NormalDistQuick.java

SSJ API Documentation Stochastic Simulation in Java

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ NormalDistQuick() [1/2]

◆ NormalDistQuick() [2/2]

Member Function Documentation

◆ barF() [1/2]

◆ barF() [2/2]

◆ barF01()

◆ cdf() [1/2]

◆ cdf() [2/2]

◆ cdf01()

◆ inverseF() [1/2]

◆ inverseF() [2/2]

◆ inverseF01()