Logistic {base}

R Documentation

The Logistic Distribution

Description

Density, distribution function, quantile function and random generation for the logistic distribution with parameters location and scale.

Usage

dlogis(x, location = 0, scale = 1, log = FALSE)
plogis(q, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
qlogis(p, location = 0, scale = 1, lower.tail = TRUE, log.p = FALSE)
rlogis(n, location = 0, scale = 1)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
location, scale	location and scale parameters.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X \le x], otherwise, P[X > x].

Details

If location or scale are omitted, they assume the default values of 0 and 1 respectively.

The Logistic distribution with location = \mu and scale = \sigma has distribution function

F(x) = \frac{1}{1 + e^{-(x-\mu)/\sigma}}%

and density

f(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.

Value

dlogis gives the density, plogis gives the distribution function, qlogis gives the quantile function, and rlogis generates random deviates.

Examples

eps <- 100 * .Machine$double.eps
x <- c(0:4, rlogis(100))
all.equal(plogis(x),                 1 / (1 + exp(-x)), tol = eps)
all.equal(plogis(x, lower=FALSE),   exp(-x)/ (1 + exp(-x)), tol = eps)
all.equal(plogis(x, lower=FALSE, log=TRUE), -log(1 + exp(x)),  tol = eps)
all.equal(dlogis(x), exp(x) * (1 + exp(x))^-2, tol = eps)

var(rlogis(4000, 0, s = 5))# approximately (+/- 3)
pi^2/3 * 5^2

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