smile.stat.distribution

Class LogisticDistribution

java.lang.Object

smile.stat.distribution.AbstractDistribution

smile.stat.distribution.LogisticDistribution

All Implemented Interfaces:

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 cumulative distribution function of the logistic distribution is given by:

                   1
 F(x; μ,s) = -------------
              1 + e-(x-μ)/s
 

The probability density function of the logistic distribution is given by:

                  e-(x-μ)/s
 f(x; μ,s) = -----------------
              s(1 + e-(x-μ)/s)2
 

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.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
double	cdf(double x) Cumulative distribution function.
double	entropy() Shannon entropy 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.
int	npara() The number of parameters of the 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.
java.lang.String	toString()
double	var() The variance of distribution.

Methods inherited from class smile.stat.distribution.AbstractDistribution

likelihood, logLikelihood

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

LogisticDistribution

public LogisticDistribution(double mu,
                            double scale)

Constructor.

Method Detail

npara

public int npara()

Description copied from interface: Distribution

The number of parameters of the distribution.

mean

public double mean()

Description copied from interface: Distribution

The mean of distribution.

var

public double var()

Description copied from interface: Distribution

The variance of distribution.

sd

public double sd()

Description copied from interface: Distribution

The standard deviation of distribution.

entropy

public double entropy()

Description copied from interface: Distribution

Shannon entropy of the distribution.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

rand

public double rand()

Description copied from interface: Distribution

Generates a random number following this distribution.

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.

logp

public double logp(double x)

Description copied from interface: Distribution

The density at x in log scale, which may prevents the underflow problem.

cdf

public double cdf(double x)

Description copied from interface: Distribution

Cumulative distribution function. That is the probability to the left of x.

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.