smile.stat.distribution

## Class LogisticDistribution

• All Implemented Interfaces:
java.io.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 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.
Serialized Form
• ### Field Summary

Fields
Modifier and Type Field and Description
`double` `mu`
The location parameter.
`double` `scale`
The scale parameter.
• ### Constructor Summary

Constructors
Constructor and Description
```LogisticDistribution(double mu, double scale)```
Constructor.
• ### Method Summary

All Methods
Modifier and Type Method and 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.
`java.lang.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 Detail

• #### mu

`public final double mu`
The location parameter.
• #### scale

`public final double scale`
The scale parameter.
• ### Constructor Detail

• #### LogisticDistribution

```public LogisticDistribution(double mu,
double scale)```
Constructor.
• ### Method Detail

• #### 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.
• #### mean

`public double mean()`
Description copied from interface: `Distribution`
The mean of distribution.
• #### variance

`public double variance()`
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.