SSJ
V. 1.2.5.

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

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) = 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 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).
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 in table x[i], i = 0, 1,…, n - 1.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Estimates and returns the parameters [hat(μ), hat(σ)] of the log-normal distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.
 double getMean()
          Returns the mean of the distribution function.
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.
 double getMu()
          Returns the parameter μ of this object.
 double getSigma()
          Returns the parameter σ of this object.
 double getStandardDeviation()
          Returns the standard deviation of the distribution function.
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 of the distribution function.
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)
          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

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


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.


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 in table 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

getMaximumLikelihoodEstimate

public static double[] getMaximumLikelihoodEstimate(double[] x,
                                                    int n)
Estimates and returns the parameters [hat(μ), hat(σ)] of the log-normal distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.

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)]

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.


SSJ
V. 1.2.5.

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