# Logis-class

From distr v2.3.1
by Peter Ruckdeschel

##### Class "Logis"

The Logistic distribution with `location`

$= \mu$,
by default `= 0`

, and `scale`

$= \sigma$, by default `= 1`

,
has distribution function
$$p(x) = \frac{1}{1 + e^{-(x-\mu)/\sigma}}$$ and density
$$d(x)= \frac{1}{\sigma}\frac{e^{(x-\mu)/\sigma}}{(1 + e^{(x-\mu)/\sigma})^2}$$
It is a long-tailed distribution with mean $\mu$ and variance
$\pi^2/3 \sigma^2$. C.f. `rlogis`

- Keywords
- distribution

##### Objects from the Class

Objects can be created by calls of the form `Logis(location, scale)`

.
This object is a logistic distribution.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### concept

- absolutely continuous distribution
- Logistic distribution
- S4 distribution class
- location scale family

##### See Also

`LogisParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rlogis`

##### Examples

```
L <- Logis(location = 1,scale = 1)
# L is a logistic distribution with location = 1 and scale = 1.
r(L)(1) # one random number generated from this distribution, e.g. 5.87557
d(L)(1) # Density of this distribution is 0.25 for x = 1.
p(L)(1) # Probability that x < 1 is 0.5.
q(L)(.1) # Probability that x < -1.197225 is 0.1.
location(L) # location of this distribution is 1.
location(L) <- 2 # location of this distribution is now 2.
```

*Documentation reproduced from package distr, version 2.3.1, License: LGPL-3*

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