location and scale.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)length(n) > 1, the length
is taken to be the number required.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.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
\(\pi^2/3 \sigma^2\).var(rlogis(4000, 0, scale = 5)) # approximately (+/- 3)
pi^2/3 * 5^2
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