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)vector of quantiles.
vector of probabilities.
number of observations. If length(n) > 1, the length
is taken to be the number required.
location and scale parameters.
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).
dlogis gives the density,
plogis gives the distribution function,
qlogis gives the quantile function, and
rlogis generates random deviates.
The length of the result is determined by n for
rlogis, and is the maximum of the lengths of the
numerical arguments for the other functions.
The numerical arguments other than n are recycled to the
length of the result. Only the first elements of the logical
arguments are used.
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 \(\pi^2/3 \sigma^2\).
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.
Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, volume 2, chapter 23. Wiley, New York.
Distributions for other standard distributions.
var(rlogis(4000, 0, scale = 5)) # approximately (+/- 3)
pi^2/3 * 5^2
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