stats (version 3.5.1)

Logistic: 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 length(n) > 1, the length is taken to be the number required.

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 \(P[X \le x]\), otherwise, \(P[X > x]\).

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.

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 \(\pi^2/3 \sigma^2\).

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

# NOT RUN {
var(rlogis(4000, 0, scale = 5))  # approximately (+/- 3)
pi^2/3 * 5^2
# }