Logistic Distribution

DESCRIPTION:

Density, cumulative probability, quantiles and random generation for the logistic distribution.

USAGE:

dlogis(x, location=0, scale=1, log=F) 
plogis(q, location=0, scale=1) 
qlogis(p, location=0, scale=1) 
rlogis(n, location=0, scale=1, bigdata=F) 

REQUIRED ARGUMENTS:

x
vector or bdVector of quantiles. Missing values ( NAs) are allowed.
q
vector or bdVector of quantiles. Missing values ( NAs) are allowed.
p
vector or bdVector 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 or bdVector of location parameters. This is replicated to be the same length as p or q or the number of deviates generated.
scale
vector or bdVector of scale parameters. This is replicated to be the same length as p or q or the number of deviates generated.
bigdata
a logical value; if TRUE, an object of type bdVector is returned. Otherwise, a vector object is returned. This argument can be used only if the bigdata library section has been loaded.
log
a logical scalar; if TRUE, dlogis will return the log of the density, not the density itself.

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.

For details on the uniform random number generator implemented in S-PLUS, see the set.seed help file.

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:

.

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)