umontreal.iro.lecuyer.probdist

Class NormalDistQuick

java.lang.Object

umontreal.iro.lecuyer.probdist.ContinuousDistribution

umontreal.iro.lecuyer.probdist.NormalDist

umontreal.iro.lecuyer.probdist.NormalDistQuick

All Implemented Interfaces:

Distribution

public class NormalDistQuick
extends NormalDist

A variant of the class NormalDist (for the normal distribution with mean μ and variance σ²). 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.

Field Summary

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

decPrec

Constructor Summary

Constructors

Constructor and Description
NormalDistQuick() Constructs a NormalDistQuick object with default parameters μ = 0 and σ = 1.
NormalDistQuick(double mu, double sigma) Constructs a NormalDistQuick object with mean μ = mu and standard deviation σ = sigma.

Method Summary

Methods

Modifier and Type	Method and Description
double	barF(double x) Returns the complementary distribution function.
static double	barF(double mu, double sigma, double x) Returns an approximation of 1 - Φ(x), where Φ 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).
double	cdf(double x) Returns the distribution function F(x).
static double	cdf(double mu, double sigma, double x) Returns an approximation of Φ(x), where Φ is the standard normal distribution function, with mean 0 and variance 1.
static double	cdf01(double x) Same as cdf (0.0, 1.0, x).
double	inverseF(double u) Returns the inverse distribution function x = F-1(u).
static double	inverseF(double mu, double sigma, double u) Returns an approximation of Φ-1(u), where Φ 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).

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

density, density, density01, getInstanceFromMLE, getMaximumLikelihoodEstimate, getMean, getMean, getMLE, getMu, getParams, getSigma, getStandardDeviation, getStandardDeviation, getVariance, getVariance, setParams, toString

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

NormalDistQuick

public NormalDistQuick()

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

NormalDistQuick

public NormalDistQuick(double mu,
               double sigma)

Constructs a NormalDistQuick object with mean μ = mu and standard deviation σ = sigma.

Method Detail

cdf

public double cdf(double x)

Description copied from interface: Distribution

Returns the distribution function F(x).

Specified by:

cdf in interface Distribution

Overrides:

cdf in class NormalDist

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 NormalDist

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 NormalDist

Parameters:

u - value at which the inverse distribution function is evaluated

Returns:

the inverse distribution function evaluated at u

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)

Returns an approximation of Φ(x), where Φ is the standard normal distribution function, with mean 0 and variance 1. Uses Marsaglia et al's fast method with table lookups. Returns 15 decimal digits of precision. This method is approximately 60% faster than NormalDist.cdf.

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)

Returns an approximation of 1 - Φ(x), where Φ is the standard normal distribution function, with mean 0 and variance 1. Uses Marsaglia et al's fast method with table lookups. Returns 15 decimal digits of precision. This method is approximately twice faster than NormalDist.barF.

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)

Returns an approximation of Φ^-1(u), where Φ is the standard normal distribution function, with mean 0 and variance 1. Uses the method of Marsaglia, Zaman, and Marsaglia, with table lookups. Returns 6 decimal digits of precision. This method is approximately 20% faster than NormalDist.inverseF.