Logis-class: Class "Logis" In distr: Object Oriented Implementation of Distributions

Description

The Logistic distribution with `location` = m, by default `= 0`, and `scale` = s, by default `= 1`, has distribution function

p(x) = 1 / (1 + exp(-(x-m)/s))

and density

d(x) = 1/s exp((x-m)/s) (1 + exp((x-m)/s))^-2.

It is a long-tailed distribution with mean m and variance pi^2 /3 s^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(s)

Thomas Stabla [email protected],
Florian Camphausen [email protected],
Peter Ruckdeschel [email protected],
Matthias Kohl [email protected]

`LogisParameter-class` `AbscontDistribution-class` `Reals-class` `rlogis`
 ```1 2 3 4 5 6 7 8 9``` ```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. ```