SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdist Class LogisticDist

```java.lang.Object
umontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.LogisticDist
```
All Implemented Interfaces:
Distribution

`public class LogisticDistextends ContinuousDistribution`

Extends the class `ContinuousDistribution` for the logistic distribution. It has location parameter α and scale parameter λ > 0. The density is

f (x) = (λe-λ(x-α))/((1 + e-λ(x-α))2)                for - ∞ < x < ∞.

and the distribution function is

F(x) = 1/[1 + e-λ(x-α)]                for - ∞ < x < ∞.

For λ = 1 and α = 0, one can write

F(x) = (1+tanh(x/2))/2.

The inverse distribution function is given by

F-1(u) = ln(u/(1 - u))/λ + α        for 0 <= u < 1.

Field Summary

Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`decPrec`

Constructor Summary
`LogisticDist()`
Constructs a LogisticDist object with default parameters α = 0 and λ = 1.
```LogisticDist(double alpha, double lambda)```
Constructs a LogisticDist object with parameters α = alpha and λ = lambda.

Method Summary
` double` `barF(double x)`
Returns the complementary distribution function.
`static double` ```barF(double alpha, double lambda, double x)```
Computes the complementary distribution function 1 - F(x).
` double` `cdf(double x)`
Returns the distribution function F(x).
`static double` ```cdf(double alpha, double lambda, double x)```
Computes the distribution function F(x).
` double` `density(double x)`
Returns f (x), the density evaluated at x.
`static double` ```density(double alpha, double lambda, double x)```
Computes the density function f (x).
` double` `getAlpha()`
Return the parameter α of this object.
`static LogisticDist` ```getInstanceFromMLE(double[] x, int n)```
Creates a new instance of a logistic distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
` double` `getLambda()`
Returns the parameter λ of this object.
` double` `getMean()`
Returns the mean.
`static double` ```getMean(double alpha, double lambda)```
Computes and returns the mean E[X] = α of the logistic distribution with parameters α and λ.
`static double[]` ```getMLE(double[] x, int n)```
Estimates the parameters (α, λ) of the logistic distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
` double[]` `getParams()`
Return a table containing the parameters of the current distribution.
` double` `getStandardDeviation()`
Returns the standard deviation.
`static double` ```getStandardDeviation(double alpha, double lambda)```
Computes and returns the standard deviation of the logistic distribution with parameters α and λ.
` double` `getVariance()`
Returns the variance.
`static double` ```getVariance(double alpha, double lambda)```
Computes and returns the variance Var[X] = π2/(3λ2) of the logistic distribution with parameters α and λ.
` double` `inverseF(double u)`
Returns the inverse distribution function x = F-1(u).
`static double` ```inverseF(double alpha, double lambda, double u)```
Computes the inverse distribution function F-1(u).
` void` ```setParams(double alpha, double lambda)```
Sets the parameters α and λ of this object.
` String` `toString()`

Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
`getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

Constructor Detail

### LogisticDist

`public LogisticDist()`
Constructs a LogisticDist object with default parameters α = 0 and λ = 1.

### LogisticDist

```public LogisticDist(double alpha,
double lambda)```
Constructs a LogisticDist object with parameters α = alpha and λ = lambda.

Method Detail

### density

`public double density(double x)`
Description copied from class: `ContinuousDistribution`
Returns f (x), the density evaluated at x.

Specified by:
`density` in class `ContinuousDistribution`
Parameters:
`x` - value at which the density is evaluated
Returns:
density function evaluated at x

### cdf

`public double cdf(double x)`
Description copied from interface: `Distribution`
Returns the distribution function F(x).

Parameters:
`x` - value at which the distribution function is evaluated
Returns:
distribution function evaluated at x

### barF

`public double barF(double x)`
Description copied from class: `ContinuousDistribution`
Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:
`barF` in interface `Distribution`
Overrides:
`barF` in class `ContinuousDistribution`
Parameters:
`x` - value at which the complementary distribution function is evaluated
Returns:
complementary distribution function evaluated at x

### inverseF

`public double inverseF(double u)`
Description copied from class: `ContinuousDistribution`
Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].

Specified by:
`inverseF` in interface `Distribution`
Overrides:
`inverseF` in class `ContinuousDistribution`
Parameters:
`u` - value at which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

### getMean

`public double getMean()`
Description copied from class: `ContinuousDistribution`
Returns the mean.

Specified by:
`getMean` in interface `Distribution`
Overrides:
`getMean` in class `ContinuousDistribution`
Returns:
the mean

### getVariance

`public double getVariance()`
Description copied from class: `ContinuousDistribution`
Returns the variance.

Specified by:
`getVariance` in interface `Distribution`
Overrides:
`getVariance` in class `ContinuousDistribution`
Returns:
the variance

### getStandardDeviation

`public double getStandardDeviation()`
Description copied from class: `ContinuousDistribution`
Returns the standard deviation.

Specified by:
`getStandardDeviation` in interface `Distribution`
Overrides:
`getStandardDeviation` in class `ContinuousDistribution`
Returns:
the standard deviation

### density

```public static double density(double alpha,
double lambda,
double x)```
Computes the density function f (x).

### cdf

```public static double cdf(double alpha,
double lambda,
double x)```
Computes the distribution function F(x).

### barF

```public static double barF(double alpha,
double lambda,
double x)```
Computes the complementary distribution function 1 - F(x).

### inverseF

```public static double inverseF(double alpha,
double lambda,
double u)```
Computes the inverse distribution function F-1(u).

### getMLE

```public static double[] getMLE(double[] x,
int n)```
Estimates the parameters (α, λ) of the logistic distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [α, λ].

Parameters:
`x` - the list of observations used to evaluate parameters
`n` - the number of observations used to evaluate parameters
Returns:
returns the parameter [ hat(α), hat(λ)]

### getInstanceFromMLE

```public static LogisticDist getInstanceFromMLE(double[] x,
int n)```
Creates a new instance of a logistic distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.

Parameters:
`x` - the list of observations to use to evaluate parameters
`n` - the number of observations to use to evaluate parameters

### getMean

```public static double getMean(double alpha,
double lambda)```
Computes and returns the mean E[X] = α of the logistic distribution with parameters α and λ.

Returns:
the mean of the logistic distribution E[X] = α

### getVariance

```public static double getVariance(double alpha,
double lambda)```
Computes and returns the variance Var[X] = π2/(3λ2) of the logistic distribution with parameters α and λ.

Returns:
the variance of the logistic distribution Var[X] = 1/3π2*(1/λ2)

### getStandardDeviation

```public static double getStandardDeviation(double alpha,
double lambda)```
Computes and returns the standard deviation of the logistic distribution with parameters α and λ.

Returns:
the standard deviation of the logistic distribution

### getAlpha

`public double getAlpha()`
Return the parameter α of this object.

### getLambda

`public double getLambda()`
Returns the parameter λ of this object.

### setParams

```public void setParams(double alpha,
double lambda)```
Sets the parameters α and λ of this object.

### getParams

`public double[] getParams()`
Return a table containing the parameters of the current distribution. This table is put in regular order: [α, λ].

### toString

`public String toString()`
Overrides:
`toString` in class `Object`

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.