Logistic {base} | R Documentation |
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.
dlogis(x, location=0, scale=1) plogis(q, location=0, scale=1) qlogis(p, location=0, scale=1) 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. |
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.
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