| Logistic {stats} | 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 |
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
|
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.
Note
qlogis(p) is the same as the well known ‘logit’
function, logit(p) = \log(p/(1-p)), and plogis(x) has
consequently been called the ‘inverse logit’.
The distribution function is a rescaled hyperbolic tangent,
plogis(x) == (1+ tanh(x/2))/2, and it is called a
sigmoid function in contexts such as neural networks.
Source
[dpr]logis are calculated directly from the definitions.
rlogis uses inversion.
References
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.
Examples
var(rlogis(4000, 0, scale = 5))# approximately (+/- 3)
pi^2/3 * 5^2