SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class LognormalDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.LognormalDist
All Implemented Interfaces:
Distribution
Direct Known Subclasses:
LognormalDistFromMoments

public class LognormalDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the lognormal distribution. (See also the Johnson SL distribution JohnsonSLDist in this package.) 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) = eμ+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 the complementary distribution function.
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)
          Returns the distribution function F(x).
static double cdf(double mu, double sigma, double x)
          Computes the lognormal distribution function, using NormalDist.cdf01.
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double mu, double sigma, double x)
          Computes the lognormal density function f (x).
static LognormalDist getInstanceFromMLE(double[] x, int n)
          Creates a new instance of a lognormal distribution with parameters μ and σ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
 double getMean()
          Returns the mean.
static double getMean(double mu, double sigma)
          Computes and returns the mean E[X] = eμ+σ2/2 of the lognormal distribution with parameters μ and σ.
static double[] getMLE(double[] x, int n)
          Estimates the parameters (μ, σ) of the lognormal distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
 double getMu()
          Returns the parameter μ of this object.
 double[] getParams()
          Returns a table containing the parameters of the current distribution, in the order: [μ, σ].
 double getSigma()
          Returns the parameter σ of this object.
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double mu, double sigma)
          Computes and returns the standard deviation of the lognormal distribution with parameters μ and σ.
 double getVariance()
          Returns the variance.
static double getVariance(double mu, double sigma)
          Computes and returns the variance Var[X] = e2μ+σ2(eσ2 - 1) of the lognormal distribution with parameters μ and σ.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
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.
 String 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

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 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
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 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 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 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 ContinuousDistribution
Parameters:
u - value at which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from class: ContinuousDistribution
Returns the mean.

Specified by:
getMean in interface Distribution
Overrides:
getMean in class ContinuousDistribution
Returns:
the mean

getVariance

public double getVariance()
Description copied from class: ContinuousDistribution
Returns the variance.

Specified by:
getVariance in interface Distribution
Overrides:
getVariance in class ContinuousDistribution
Returns:
the variance

getStandardDeviation

public double getStandardDeviation()
Description copied from class: ContinuousDistribution
Returns the standard deviation.

Specified by:
getStandardDeviation in interface Distribution
Overrides:
getStandardDeviation in class ContinuousDistribution
Returns:
the standard deviation

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 NormalDist.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.


getMLE

public static double[] getMLE(double[] x,
                              int n)
Estimates the parameters (μ, σ) of the lognormal distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [μ, σ].

Parameters:
x - the list of observations used to evaluate parameters
n - the number of observations used to evaluate parameters
Returns:
returns the parameters [hat(μ), hat(σ)]

getInstanceFromMLE

public static LognormalDist getInstanceFromMLE(double[] x,
                                               int n)
Creates a new instance of a lognormal distribution with parameters μ and σ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.

Parameters:
x - the list of observations to use to evaluate parameters
n - the number of observations to use to evaluate parameters

getMean

public static double getMean(double mu,
                             double sigma)
Computes and returns the mean E[X] = eμ+σ2/2 of the lognormal distribution with parameters μ and σ.

Returns:
the mean of the lognormal distribution

getVariance

public static double getVariance(double mu,
                                 double sigma)
Computes and returns the variance Var[X] = e2μ+σ2(eσ2 - 1) of the lognormal distribution with parameters μ and σ.

Returns:
the variance of the lognormal distribution

getStandardDeviation

public static double getStandardDeviation(double mu,
                                          double sigma)
Computes and returns the standard deviation of the lognormal distribution with parameters μ and σ.

Returns:
the standard deviation of the lognormal distribution

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.


getParams

public double[] getParams()
Returns a table containing the parameters of the current distribution, in the order: [μ, σ].


toString

public String toString()
Overrides:
toString in class Object

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.