distr (version 2.9.5)

Logis-class: Class "Logis"

Description

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

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.

Author

Thomas Stabla ,
Florian Camphausen ,
Peter Ruckdeschel ,
Matthias Kohl

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.
## 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.