Package elki.math.statistics.distribution

Class LogNormalDistribution

  • All Implemented Interfaces:
    Distribution
    @Alias("lognormal")
public class LogNormalDistribution
extends java.lang.Object
implements Distribution
    Log-Normal distribution. The parameterization of this class is somewhere inbetween of GNU R and SciPy. Similar to GNU R we use the logmean and logstddev. Similar to Scipy, we also have a location parameter that shifts the distribution. Our implementation maps to SciPy's as follows: scipy.stats.lognorm(logstddev, shift, FastMath.exp(logmean))
    Since:
    0.5.0
    Author:
    Erich Schubert

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private double logmean
      Mean value for the generator
      private double logstddev
      Standard deviation
      private double shift
      Additional shift factor

    • Constructor Summary

      Constructors 
      Constructor Description
      LogNormalDistribution​(double logmean, double logstddev, double shift)
      Constructor for Log-Normal distribution

    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double cdf​(double val)
      Return the cumulative density function at the given value.
      static double cdf​(double x, double mu, double sigma)
      Cumulative probability density function (CDF) of a normal distribution.
      double getLogMean()
      Get the log mean value.
      double getLogStddev()
      Get the log standard deviation.
      double getShift()
      Get the distribution shift.
      double logpdf​(double val)
      Return the log density of an existing value
      static double logpdf​(double x, double mu, double sigma)
      Probability density function of the normal distribution.
      double nextRandom​(java.util.Random random)
      Generate a new random value
      double pdf​(double val)
      Return the density of an existing value
      static double pdf​(double x, double mu, double sigma)
      Probability density function of the normal distribution.
      double quantile​(double val)
      Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
      static double quantile​(double x, double mu, double sigma)
      Inverse cumulative probability density function (probit) of a normal distribution.
      java.lang.String toString()
      Describe the distribution

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

    • Field Detail

      • logmean

        private double logmean
        Mean value for the generator

      • logstddev

        private double logstddev
        Standard deviation

      • shift

        private double shift
        Additional shift factor

    • Constructor Detail

      • LogNormalDistribution

        public LogNormalDistribution​(double logmean,
                             double logstddev,
                             double shift)
        Constructor for Log-Normal distribution
        Parameters:
        logmean - Mean
        logstddev - Standard Deviation
        shift - Shifting offset

    • Method Detail

      • getLogMean

        public double getLogMean()
        Get the log mean value.
        Returns:
        logmean

      • getLogStddev

        public double getLogStddev()
        Get the log standard deviation.
        Returns:
        log standard deviation

      • getShift

        public double getShift()
        Get the distribution shift.
        Returns:
        Shift

      • pdf

        public double pdf​(double val)
        Description copied from interface: Distribution
        Return the density of an existing value
        Specified by:
        pdf in interface Distribution
        Parameters:
        val - existing value
        Returns:
        distribution density

      • logpdf

        public double logpdf​(double val)
        Description copied from interface: Distribution
        Return the log density of an existing value
        Specified by:
        logpdf in interface Distribution
        Parameters:
        val - existing value
        Returns:
        log distribution density

      • cdf

        public double cdf​(double val)
        Description copied from interface: Distribution
        Return the cumulative density function at the given value.
        Specified by:
        cdf in interface Distribution
        Parameters:
        val - existing value
        Returns:
        cumulative density

      • quantile

        public double quantile​(double val)
        Description copied from interface: Distribution
        Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
        Specified by:
        quantile in interface Distribution
        Parameters:
        val - Quantile to find
        Returns:
        Quantile position

      • pdf

        public static double pdf​(double x,
                         double mu,
                         double sigma)
        Probability density function of the normal distribution. 
         1/(SQRT(2*pi)*sigma*x) * e^(-log(x-mu)^2/2sigma^2)
        Parameters:
        x - The value.
        mu - The mean.
        sigma - The standard deviation.
        Returns:
        PDF of the given normal distribution at x.

      • logpdf

        public static double logpdf​(double x,
                            double mu,
                            double sigma)
        Probability density function of the normal distribution. 
         1/(SQRT(2*pi)*sigma*x) * e^(-log(x-mu)^2/2sigma^2)
        Parameters:
        x - The value.
        mu - The mean.
        sigma - The standard deviation.
        Returns:
        logPDF of the given normal distribution at x.

      • cdf

        public static double cdf​(double x,
                         double mu,
                         double sigma)
        Cumulative probability density function (CDF) of a normal distribution.
        Parameters:
        x - value to evaluate CDF at
        mu - Mean value
        sigma - Standard deviation.
        Returns:
        The CDF of the given normal distribution at x.

      • quantile

        public static double quantile​(double x,
                              double mu,
                              double sigma)
        Inverse cumulative probability density function (probit) of a normal distribution.
        Parameters:
        x - value to evaluate probit function at
        mu - Mean value
        sigma - Standard deviation.
        Returns:
        The probit of the given normal distribution at x.

      • nextRandom

        public double nextRandom​(java.util.Random random)
        Description copied from interface: Distribution
        Generate a new random value
        Specified by:
        nextRandom in interface Distribution
        Parameters:
        random - Random number generator
        Returns:
        new random value

      • toString

        public java.lang.String toString()
        Description copied from interface: Distribution
        Describe the distribution
        Specified by:
        toString in interface Distribution
        Overrides:
        toString in class java.lang.Object
        Returns:
        description