This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.


The (discrete) cumulative distribution function of the Poisson distribution

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.




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 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


Was this topic helpful?