Cumulative distribution function of the logistic distribution
This functionality does not run in MATLAB.
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 floating-point number or a symbolic expression:
If x is a floating-point number and m and s can be converted to floating-point numbers, then f(x) returns a floating-point 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)
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