Cumulative distribution function of the logistic distribution
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stats::logisticCDF(m
, s
)
stats::logisticCDF(m, s)
returns a procedure
representing the cumulative distribution function
of the logistic distribution with mean m
and
standard deviation s
> 0 as
a procedure.
The procedure f := stats::logisticCDF(m, s)
can
be called in the form f(x)
with an arithmetical
expression x
. The return value of f(x)
is
either a floatingpoint number or a symbolic expression:
If x
is a floatingpoint number and m
and s
can
be converted to floatingpoint numbers, then f(x)
returns
a floatingpoint number between 0.0 and 1.0.
The call f( infinity )
returns 0
;
the call f( infinity )
returns 1
.
In all other cases, the expression 1/2*(1 + tanh(PI*(x
 m)/(2*sqrt(3)*s)))
is returned symbolically.
Numerical values for m
and s
are
only accepted if they are real and s
is positive.
The function is sensitive to the environment variable DIGITS
which
determines the numerical working precision.
We evaluate the cumulative distribution function with m
= 0 and s
= 1 at
various points:
f := stats::logisticCDF(0, 1): f(infinity), f(3), f(0.5), f(2/3), f(PI), f(infinity)
delete f:
We use symbolic arguments:
f := stats::logisticCDF(m, s): f(x)
When numerical values are assigned to m
and s
,
the function f
starts to produce numerical values:
m := 0: s := 1: f(3), f(3.0)
delete f, m, s:

The mean: an arithmetical expression representing a real value 

The standard deviation: an arithmetical expression representing a positive real value 