Package smile.stat.distribution

Class LogisticDistribution

java.lang.Object
smile.stat.distribution.AbstractDistribution
smile.stat.distribution.LogisticDistribution
All Implemented Interfaces:
Serializable, Distribution
public class LogisticDistribution extends AbstractDistribution
The logistic distribution is a continuous probability distribution whose cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis).

The logistic distribution and the S-shaped pattern that results from it have been extensively used in many different areas such as:

  • Biology - to describe how species populations grow in competition.
  • Epidemiology - to describe the spreading of epidemics.
  • Psychology - to describe learning.
  • Technology - to describe how new technologies diffuse and substitute for each other.
  • Market - the diffusion of new-product sales.
  • Energy - the diffusion and substitution of primary energy sources.
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    final double
    mu
    The location parameter.
    final double
    scale
    The scale parameter.

  • Constructor Summary

    Constructors
    Constructor
    Description
    LogisticDistribution(double mu, double scale)
    Constructor.

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    cdf(double x)
    Cumulative distribution function.
    double
    entropy()
    Shannon entropy of the distribution.
    int
    length()
    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()
    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.
    double
    sd()
    The standard deviation of distribution.
    String
    toString()
     
    double
    variance()
    The variance of distribution.

    Methods inherited from class smile.stat.distribution.AbstractDistribution

    inverseTransformSampling, quantile, quantile, rejection

    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

    likelihood, logLikelihood, rand

  • Field Details

    • mu

      public final double mu
      The location parameter.

    • scale

      public final double scale
      The scale parameter.

  • Constructor Details

    • LogisticDistribution

      public LogisticDistribution(double mu, double scale)
      Constructor.
      Parameters:
      mu - the location parameter.
      scale - the scale parameter.

  • Method Details

    • length

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

    • mean

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

    • variance

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

    • sd

      public double sd()
      Description copied from interface: Distribution
      The standard deviation of distribution.
      Returns:
      The standard deviation.

    • entropy

      public double entropy()
      Description copied from interface: Distribution
      Shannon entropy of the 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.
      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.
      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.
      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.
      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.
      Parameters:
      p - the probability.
      Returns:
      the quantile.