LogisticDistribution (Smile Math 1.0.3 API)

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.
Author:

Haifeng Li

Constructor Summary

Constructors
Constructor and Description

LogisticDistribution(double mu, double scale)
Constructor.

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

Method Summary

Methods
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.
`String`	`toString()`
`double`	`var()` The variance of distribution.

Methods inherited from class smile.stat.distribution.AbstractDistribution
inverseTransformSampling, likelihood, logLikelihood, quantile, quantile, rejection

Methods inherited from class java.lang.Object
clone, equals, finalize, 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 String toString()
```
    Overrides:
    
    toString in class 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.

Class LogisticDistribution

Constructor Summary

Method Summary

Methods inherited from class smile.stat.distribution.AbstractDistribution

Methods inherited from class java.lang.Object

Constructor Detail

LogisticDistribution

Method Detail

npara

mean

var

sd

entropy

toString

rand

p

logp

cdf

quantile