# 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.
• ## 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.