umontreal.iro.lecuyer.probdist
Class LognormalDist

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

All Implemented Interfaces:

Distribution

public class LognormalDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the lognormal distribution. It has scale parameter μ and shape parameter σ > 0. The density is

f (x) = ((2π)^1/2σx)^-1e^{-(ln(x)-μ)2/(2σ2)} for x > 0,

and 0 elsewhere. The distribution function is

F(x) = Φ((ln(x)-μ)/σ) for x > 0,

where Φ is the standard normal distribution function. Its inverse is given by

F^-1(u) = e^μ+σΦ-1(u) for 0 <= u < 1.

If ln(Y) has a normal distribution, then Y has a lognormal distribution with the same parameters.

This class relies on the methods NormalDist.cdf01 and NormalDist.inverseF01 of NormalDist to approximate Φ and Φ^-1.

Field Summary

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

decPrec

Constructor Summary

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

LognormalDist(double mu, double sigma)
Constructs a LognormalDist 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 lognormal complementary distribution function bar(F)(x), using NormalDist.barF01.
double	cdf(double x) Computes and returns the distribution function F(x).
static double	cdf(double mu, double sigma, double x) Computes the lognormal distribution function, using cdf01.
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 lognormal density function f (x).
double	getMu() Returns the parameter μ of this object.
double	getSigma() Returns the parameter σ of this object.
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 of the lognormal distribution function, using NormalDist.inverseF01.
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

LognormalDist

public LognormalDist()

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

LognormalDist

public LognormalDist(double mu,
                     double sigma)

Constructs a LognormalDist 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 lognormal density function f (x).

cdf

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

Computes the lognormal distribution function, using cdf01.

barF

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

Computes the lognormal complementary distribution function bar(F)(x), using NormalDist.barF01.

inverseF

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

Computes the inverse of the lognormal distribution function, using NormalDist.inverseF01.

getMu

public double getMu()

Returns the parameter μ of this object.

getSigma

public double getSigma()

Returns the parameter σ of this object.

setParams

public void setParams(double mu,
                      double sigma)

Sets the parameters μ and σ of this object.