umontreal.iro.lecuyer.probdist
Class NormalDist

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

All Implemented Interfaces:

Distribution

Direct Known Subclasses:

NormalDistQuick

public class NormalDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the normal distribution (e.g.,). It has mean μ and variance σ². Its density function is

f (x) = e^{-(x-μ)2/(2σ2)}/((2π)^1/2σ) for - ∞ < x < ∞,

where σ > 0. When μ = 0 and σ = 1, we have the standard normal distribution, with corresponding distribution function

F(x) = Φ(x) = ∫_-∞^xe^-t2/2 dt/(2π)^1/2 for - ∞ < x < ∞.

The non-static methods cdf, barF, and inverseF are implemented via cdf01, barF01, and inverseF01, respectively.

Field Summary

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

decPrec

Constructor Summary

NormalDist()
Constructs a NormalDist object with default parameters μ = 0 and σ = 1.

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

Method Summary

double	barF(double x) Returns bar(F)(x) = 1 - F(x).
static double	barF(double mu, double sigma, double x) Computes the complementary normal distribution function bar(F)(x) = 1 - Φ((x - μ)/σ), with mean μ and variance σ.
static double	barF01(double x) Same as barF (0.0, 1.0, x).
double	cdf(double x) Computes and returns the distribution function F(x).
static double	cdf(double mu, double sigma, double x) Computes the normal distribution function with mean μ and variance σ2.
static double	cdf01(double x) Same as cdf (0.0, 1.0, x).
double	density(double x) Returns f (x), the density of X evaluated at x.
static double	density(double mu, double sigma, double x) Computes the normal density function.
double	getMu() Returns the parameter μ.
double	getSigma() Returns the parameter σ.
double	inverseF(double u) Computes and returns the inverse distribution function F-1(u), defined in.
static double	inverseF(double mu, double sigma, double u) Computes the inverse normal distribution function with mean μ and variance σ2.
static double	inverseF01(double u) Same as inverseF (0.0, 1.0, u).
void	setParams(double mu, double sigma) Sets the parameters μ and σ of this object.

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution

inverseBisection, inverseBrent

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NormalDist

public NormalDist()

Constructs a NormalDist object with default parameters μ = 0 and σ = 1.

NormalDist

public NormalDist(double mu,
                  double sigma)

Constructs a NormalDist 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 of X 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

Computes and 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 interface: Distribution

Returns 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 interface: Distribution

Computes and returns the inverse distribution function F^-1(u), defined in.

Specified by:

inverseF in interface Distribution

Overrides:

inverseF in class ContinuousDistribution

Parameters:

u - value in the interval (0, 1) for which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

density

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

Computes the normal density function.

cdf01

public static double cdf01(double x)

Same as cdf (0.0, 1.0, x).

cdf

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

Computes the normal distribution function with mean μ and variance σ². Uses the Chebyshev approximation , which gives 16 decimals of precision.

barF01

public static double barF01(double x)

Same as barF (0.0, 1.0, x).

barF

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

Computes the complementary normal distribution function bar(F)(x) = 1 - Φ((x - μ)/σ), with mean μ and variance σ. Uses a Chebyshev series giving 16 decimal digits of precision.

inverseF01

public static double inverseF01(double u)

Same as inverseF (0.0, 1.0, u).

inverseF

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

Computes the inverse normal distribution function with mean μ and variance σ². Uses rational Chebyshev approximations giving at least 16 decimal digits of precision.

getMu

public double getMu()

Returns the parameter μ.

getSigma

public double getSigma()

Returns the parameter σ.

setParams

public void setParams(double mu,
                      double sigma)

Sets the parameters μ and σ of this object.