Cumulative distribution function of the logistic distribution

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.


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 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.

Environment Interactions

The function is sensitive to the environment variable DIGITS which determines the numerical working precision.


Example 1

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:

Example 2

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

Return Values


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