This is machine translation

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


The (discrete) cumulative distribution function of the geometric 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::geometricCDF(p) returns a procedure representing the (discrete) cumulative distribution function

of the geometric distribution with 'probability parameter' p.

The procedure f:=stats::geometricCDF(p) can be called in the form f(x) with an arithmetical expression x. The return value of f(x) is either a number or a symbolic expression:

If x < 1 can be decided, then f(x) returns 0. If x ≥ 1 can be decided, then f(x) returns the value .

If x is a floating-point number and p can be converted to a floating-point number, then these values are returned as floating-point numbers. Otherwise, symbolic expressions are returned.

The function f reacts to properties of identifiers set via assume. If x is a symbolic expression with the property x < 1 or x ≥ 1, the corresponding values are returned.

f(x) returns the symbolic call stats::geometricCDF(p)(x) if neither x < 1 nor x ≥ 1 can be decided.

If p = 0 or p = 0.0, then f(x) returns 0 or 0.0, respectively, for any value of x.

Numerical values for p are only accepted if they satisfy 0 ≤ p ≤ 1.

If x is a real floating-point number, f(x) produces a floating number provided p is a numerical value. If x is an exact numerical value, no internal floating-point conversion of the parameter p is attempted.

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 at various points:

f := stats::geometricCDF(1/3):
f(-PI) = f(float(-PI)), f(1) = f(1.0), f(103/10) = f(10.3)

delete f:

Example 2

If x is a symbolic object without properties, then it cannot be decided whether x ≥ 1 holds. A symbolic function call is returned:

f := stats::geometricCDF(p): f(x)

With suitable properties, it can be decided whether x ≥ 1 holds. An explicit expression is returned:

assume(1 <= x): f(x)

unassume(x): delete f:

Example 3

We use symbolic arguments:

f := stats::geometricCDF(p): f(x)

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

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

When numerical values are assigned to p, the function f starts to produce numbers if the argument is numerical:

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

delete f, p:



The 'probability parameter': an arithmetical expression representing a real number 0 ≤ p ≤ 1.

Return Values



The geometric distribution describes the number of Bernoulli trials with success probability p up to and including the first success.

Was this topic helpful?