Package smile.stat.distribution

Class LogNormalDistribution

java.lang.Object
smile.stat.distribution.LogNormalDistribution
All Implemented Interfaces:
Serializable, Distribution
public class LogNormalDistribution extends Object implements Distribution
A log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. The log-normal distribution is the single-tailed probability distribution of any random variable whose logarithm is normally distributed. If X is a random variable with a normal distribution, then Y = exp(X) has a log-normal distribution; likewise, if Y is log-normally distributed, then log(Y) is normally distributed. A variable might be modeled as log-normal if it can be thought of as the multiplicative product of many independent random variables each of which is positive.
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    final double
    mean
    The mean.
    final double
    mu
    The mean of normal distribution.
    final double
    sigma
    The standard deviation of normal distribution.

  • Constructor Summary

    Constructors
    Constructor
    Description
    LogNormalDistribution(double mu, double sigma)
    Constructor.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(double x)
    Cumulative distribution function.
    double
    entropy()
    Returns Shannon entropy of the distribution.
    static LogNormalDistribution
    fit(double[] data)
    Estimates the distribution parameters by MLE.
    int
    length()
    Returns the number of parameters of the distribution.
    double
    logp(double x)
    The density at x in log scale, which may prevents the underflow problem.
    double
    mean()
    Returns the mean of distribution.
    double
    p(double x)
    The probability density function for continuous distribution or probability mass function for discrete distribution at x.
    double
    quantile(double p)
    The quantile, the probability to the left of quantile is p.
    double
    rand()
    Generates a random number following this distribution.
    String
    toString()
     
    double
    variance()
    Returns the variance of distribution.

    Methods inherited from class java.lang.Object

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

    Methods inherited from interface smile.stat.distribution.Distribution

    inverseTransformSampling, likelihood, logLikelihood, quantile, quantile, rand, rejectionSampling, sd

  • Field Details

    • mu

      public final double mu
      The mean of normal distribution.

    • sigma

      public final double sigma
      The standard deviation of normal distribution.

    • mean

      public final double mean
      The mean.

  • Constructor Details

    • LogNormalDistribution

      public LogNormalDistribution(double mu, double sigma)
      Constructor.
      Parameters:
      mu - the mean of normal distribution.
      sigma - the standard deviation of normal distribution.

  • Method Details

    • fit

      public static LogNormalDistribution fit(double[] data)
      Estimates the distribution parameters by MLE.
      Parameters:
      data - the training data.
      Returns:
      the distribution.

    • length

      public int length()
      Description copied from interface: Distribution
      Returns the number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.
      Specified by:
      length in interface Distribution
      Returns:
      The number of parameters.

    • mean

      public double mean()
      Description copied from interface: Distribution
      Returns the mean of distribution.
      Specified by:
      mean in interface Distribution
      Returns:
      The mean.

    • variance

      public double variance()
      Description copied from interface: Distribution
      Returns the variance of distribution.
      Specified by:
      variance in interface Distribution
      Returns:
      The variance.

    • entropy

      public double entropy()
      Description copied from interface: Distribution
      Returns Shannon entropy of the distribution.
      Specified by:
      entropy in interface Distribution
      Returns:
      Shannon entropy.

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • rand

      public double rand()
      Description copied from interface: Distribution
      Generates a random number following this distribution.
      Specified by:
      rand in interface Distribution
      Returns:
      a random number.

    • p

      public double p(double x)
      Description copied from interface: Distribution
      The probability density function for continuous distribution or probability mass function for discrete distribution at x.
      Specified by:
      p in interface Distribution
      Parameters:
      x - a real number.
      Returns:
      the density.

    • logp

      public double logp(double x)
      Description copied from interface: Distribution
      The density at x in log scale, which may prevents the underflow problem.
      Specified by:
      logp in interface Distribution
      Parameters:
      x - a real number.
      Returns:
      the log density.

    • cdf

      public double cdf(double x)
      Description copied from interface: Distribution
      Cumulative distribution function. That is the probability to the left of x.
      Specified by:
      cdf in interface Distribution
      Parameters:
      x - a real number.
      Returns:
      the probability.

    • quantile

      public double quantile(double p)
      Description copied from interface: Distribution
      The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.
      Specified by:
      quantile in interface Distribution
      Parameters:
      p - the probability.
      Returns:
      the quantile.