| 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 |
lower.tail |
logical; if |
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 is the cumulative distribution function, and
qlogis is the quantile function of the logistic distribution.
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/(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
[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