Probability function of the Poisson distribution
This functionality does not run in MATLAB.
stats::poissonPF(m) returns a procedure representing the probability function
of the Poisson distribution with mean m.
The procedure f := stats::poissonPF(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 non-integer numerical value, f(x) returns 0 or 0.0, respectively.
If x is an integer or the floating-point equivalent of an integer, then an explicit value is returned.
In all other cases, f(x) returns the symbolic call stats::poissonPF(n,p)(x).
Numerical values for m are only accepted if they are nonnegative.
If x is a floating-point number, the result is a floating-point number provided m is a nonnegative numerical value. If both x and m are exact values then the result is an exact number.
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 the procedure generated by stats::poissonPF.
The function is sensitive to the environment variable DIGITS which determines the numerical working precision.
We calculate the Poisson probability with m = 8 at various points:
f := stats::poissonPF(8): f(-1), f(-1.0), f(0), f(1/2), f(1), f(3/2), f(3) = f(float(3))
We use symbolic arguments:
f := stats::poissonPF(m): f(x)
If x is a numerical value, symbolic expressions in m are returned:
f(8), f(17/2), f(9.0), f(9.2)
When numerical values are assigned to m, the function f starts to produce numbers if the argument is numerical:
m := 3: f(8), f(17/2), f(9.0), f(9.2)
delete f, m:
The mean: an arithmetical expression representing a nonnegative real number