Cumulative distribution function of the normal distribution

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stats::normalCDF(m, v)


stats::normalCDF(m, v) returns a procedure representing the cumulative distribution function

of the normal distribution with mean m and variance v.

The procedure f := stats::normalCDF(m, v) can be called in the form f(x) with an arithmetical expression x. The value 1/2 + 1/2* erf((x - m)/sqrt(2*v)) is returned.

If x is a floating-point number and both m and v can be converted to floating-point numbers, this value is returned as a floating-point number. Otherwise, a symbolic expression is returned.

Numerical values for m and v are only accepted if they are real and v 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 mean m = 2 and variance at various points:

f := stats::normalCDF(2, 3/4):
f(-infinity), f(-3), f(PI), f(infinity)

f(-100.0), f(-3.0), f(float(PI)), f(10.0), f(100.0)

delete f:

Example 2

We use symbolic arguments:

f := stats::normalCDF(m, v): f(3), f(x)

When numerical values are assigned to m and v, the function f starts to produce numerical values:

m := 4: v := PI: f(3), f(3.0)

delete f, m, v:



The mean: an arithmetical expression representing a real value


The variance: an arithmetical expression representing a positive real value

Return Values