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 longtailed 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.
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.
Note
qlogis(p)
is the same as the well known ‘logit’
function, logit(p) = \log p/(1p)
,
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
[dpq]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.
See Also
Distributions for other standard distributions.
Examples
var(rlogis(4000, 0, scale = 5)) # approximately (+/ 3)
pi^2/3 * 5^2