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
$$f(x)= \frac{1}{\sigma}\frac{e^{(x-\mu)/\sigma}}{(1 + e^{(x-\mu)/\sigma})^2}$$
The generation algorithm uses inversion. The parameters
lb
and ub
can be used to generate variates from
the Logistic distribution truncated to the interval (lb
,ub
).