Logistic Distribution
DESCRIPTION:
Density, cumulative probability, quantiles and random generation for the logistic distribution.
USAGE: 
dlogis(x, location=0, scale=1)
plogis(q, location=0, scale=1)
qlogis(p, location=0, scale=1)
rlogis(n, location=0, scale=1)
REQUIRED ARGUMENTS:
x:
vector of quantiles. Missing values (NAs) are allowed.
q:
vector of quantiles. Missing values (NAs) are allowed.
p:
vector of probabilities. Missing values (NAs) are allowed.
n:
sample size. If length(n) is larger than 1, then length(n) random values are returned.
OPTIONAL ARGUMENTS:
location:
vector of location parameters. This is replicated to be the same length as p or q or the number of deviates generated.
scale:
vector of scale parameters. This is replicated to be the same length as p or q or the number of deviates generated.
VALUE:
density (dlogis), probability (plogis), quantile (qlogis), or random sample (rlogis) for the logistic distribution with parameters location and scale.
SIDE EFFECTS:
The function rlogis causes creation of the dataset .Random.seed if it does not already exist, otherwise its value is updated.
DETAILS:
Elements of q or p that are missing will cause the corresponding elements of the result to be missing.
BACKGROUND:
The logistic is a unimodal, symmetric distribution on the real line with tails that are longer than the Gaussian distribution. It is heavily used to model growth curves, but has also been used in bioassay studies and other applications. A motivation for using the logistic with growth curves is because the logistic distribution function F satisfies: the derivative of F with respect to x is proportional to [F(x)-A][B-F(x)] with A < B. The interpretation is that the rate of growth is proportional to the amount already grown times the amount of growth that is still expected.
REFERENCES:
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, vol. 2. Houghton-Mifflin, Boston.

Logistic Distribution. In Encyclopedia of Statistical Sciences. S. Kotz and N. L. Johnson, eds.

SEE ALSO:
set.seed .
EXAMPLES: 
# comparison of the densities of the logistic and the normal with the
# same variance
xx <- seq(-6, 6, by = 0.1)
plot(xx, dlogis(xx), type = "l", ylab="density", xlab="")
lines(xx, dnorm(xx, s = pi/sqrt(3)), lty = 2)
legend(3, .22, c("Logistic", "Gaussian"), lty=1:2)