# Logis-class

##### 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.

##### Slots

`img`

Object of class

`"Reals"`

: The space of the image of this distribution has got dimension 1 and the name "Real Space".`param`

Object of class

`"LogisParameter"`

: the parameter of this distribution (location and scale), declared at its instantiation`r`

Object of class

`"function"`

: generates random numbers (calls function rlogis)`d`

Object of class

`"function"`

: density function (calls function dlogis)`p`

Object of class

`"function"`

: cumulative function (calls function plogis)`q`

Object of class

`"function"`

: inverse of the cumulative function (calls function qlogis)`.withArith`

logical: used internally to issue warnings as to interpretation of arithmetics

`.withSim`

logical: used internally to issue warnings as to accuracy

`.logExact`

logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function

`.lowerExact`

logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

`Symmetry`

object of class

`"DistributionSymmetry"`

; used internally to avoid unnecessary calculations.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### Methods

- initialize
`signature(.Object = "Logis")`

: initialize method- location
`signature(object = "Logis")`

: returns the slot`location`

of the parameter of the distribution- location<-
`signature(object = "Logis")`

: modifies the slot`location`

of the parameter of the distribution- scale
`signature(object = "Logis")`

: returns the slot`scale`

of the parameter of the distribution- scale<-
`signature(object = "Logis")`

: modifies the slot`scale`

of the parameter of the distribution- *
`signature(e1 = "Logis", e2 = "numeric")`

- +
`signature(e1 = "Logis", e2 = "numeric")`

: For the logistic location scale family we use its closedness under affine linear transformations.

##### See Also

`LogisParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rlogis`

##### Examples

```
# NOT RUN {
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.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
location(L) # location of this distribution is 1.
location(L) <- 2 # location of this distribution is now 2.
# }
```

*Documentation reproduced from package distr, version 2.8.0, License: LGPL-3*