The (discrete) cumulative distribution function of the Poisson distribution
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stats::poissonCDF(m
)
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 floatingpoint
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 floatingpoint number if x
is
a floatingpoint 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 floatingpoint 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,
floatingpoint results are computed much faster than exact results.
If floatingpoint approximations are desired, pass a floatingpoint
number 
The function is sensitive to the environment variable DIGITS
which
determines the numerical working precision.
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:
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 