Documentation of 'umontreal.iro.lecuyer.probdist.LognormalDist' Java class
LognormalDist
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umontreal.iro.lecuyer.probdist

Class LognormalDist

  • All Implemented Interfaces:
    Distribution
    Direct Known Subclasses:
    LognormalDistFromMoments

    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.

    • Constructor Summary

      Constructors 
      Constructor and Description
      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

      All Methods Static Methods Instance Methods Concrete 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)
      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 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()
      Return a table containing the parameters of the current distribution.
      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.
      java.lang.String toString() 

      • 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

      • 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.

      • 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()
        Return a table containing the parameters of the current distribution. This table is put in regular order: [μ, σ].

      • toString

        public java.lang.String toString()
        Overrides:
        toString in class java.lang.Object
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