Logistic(base)R Documentation

The Logistic Distribution

Description

These functions provide information about the logistic distribution with parameters location and scale. dlogis gives the density, plogis gives the distribution function qlogis gives the quantile function and rlogis generates random deviates.

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

The Logistic distribution with location = m and scale = s has distribution function

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

and density

f(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.

Usage

dlogis(x, location=0, scale=1)
plogis(q, location=0, scale=1)
qlogis(p, location=0, scale=1)
rlogis(n, location=0, scale=1)

Arguments

x,q vector of quantiles.
p vector of probabilities.
n number of observations to generate.
location,scale location and scale parameters.

Examples

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