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