Cumulative distribution function of the normal distribution
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stats::normalCDF(m, v) returns a procedure
representing the cumulative distribution function
of the normal distribution with mean
f := stats::normalCDF(m, v) can
be called in the form
f(x) with an arithmetical
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.
The function is sensitive to the environment variable
determines the numerical working precision.
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)
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