Logistic {base} | R Documentation |
Density, distribution function, quantile function and random
generation for the logistic distribution with parameters
location
and scale
.
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)
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations to generate. |
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 <= x], otherwise, P[X > x]. |
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 densityf(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.
dlogis
gives the density,
plogis
gives the distribution function,
qlogis
gives the quantile function, and
rlogis
generates random deviates.
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=F), exp(-x)/ (1 + exp(-x)), tol = eps) all.equal(plogis(x, lower=F, log=T), -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