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The (discrete) cumulative distribution function of the Poisson distribution

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stats::poissonCDF(m) returns a procedure representing the (discrete) cumulative distribution function

of the Poisson distribution with mean m.

The procedure f := stats::poissonCDF(m) can be called in the form f(x) with arithmetical expressions x. The return value of f(x) is either a floating-point number, an exact numerical value, or a symbolic expression:

If x is a numerical real value, then an explicit value is returned. It is a floating-point number if x is a floating-point number and m can be converted to a positive real float. Otherwise, an exact expression is returned.

If x is a numerical value < 0, then 0, respectively 0.0, is returned for any value of m.

For symbolic values of x, f(x) returns the symbolic call stats::poissonCDF(m)(x).

Numerical values for m are only accepted if they are nonnegative.

If x is a real floating-point number, the result is a floating number provided m is a nonnegative numerical value. If both x and m are exact numerical values, the result is an exact number.

    Note:   Note that for large m, floating-point results are computed much faster than exact results. If floating-point approximations are desired, pass a floating-point number x to stats::poissonCDF!

Environment Interactions

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


Example 1

We evaluate the distribution function with m = at various points:

f := stats::poissonCDF(1/2):
f(-PI) = f(float(-PI)), f(0) = f(0.0), f(4) = f(4.0)

delete f:

Example 2

We use symbolic arguments. If x is symbolic, a symbolic call is returned:

f := stats::poissonCDF(m): f(x)

If x is a numerical value, symbolic expressions in m are returned:

f(-1), f(0), f(5/2), f(PI)

When numerical values are assigned to m, the function f starts to produce explicit results if the argument is numerical:

m := 3: f(-1), f(0), f(5/2), f(PI)

delete f, m:



The mean: an arithmetical expression representing a nonnegative real number

Return Values


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