Probability function of the Poisson distribution

Use only in the MuPAD Notebook Interface.

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.

Environment Interactions

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


Example 1

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))

delete f:

Example 2

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

Return Values


Was this topic helpful?