geometricCdf¶

Evaluates the discrete geometric cumulative distribution function (CDF).

Synopsis¶

geometricCdf (ix,  pin)

Required Arguments¶

int ix (Input): Argument for which the discrete geometric CDF is to be evaluated. ix must be non-negative.
float pin (Input): Probability parameter of the discrete geometric CDF (the probability of success for each independent trial). pin must be in the open interval (0, 1).

Return Value¶

The probability that a discrete geometric random variable takes a value less than or equal to ix. A value of NaN is returned if an input value is in error.

Description¶

The function geometricCdf evaluates the discrete geometric cumulative distribution function (CDF), defined

\[F(I|p) = \sum_{i=0}^{I} p(1-p)^i = 1 - (1-p)^{I+1}, \phantom{...} 0 < p < 1\]

where the return value F(I∣p) is the probability that up to I = ix trials would be observed before observing a success, and input parameter p = pin is the probability of success for each independent trial.

Example¶

In this example, we evaluate the discrete geometric CDF at ix = 3, pin = 0.25.

from __future__ import print_function
from numpy import *
from pyimsl.stat.geometricCdf import geometricCdf

ix = 3
pin = 0.25

p = geometricCdf(ix, pin)

print("The probability that a discrete geometric random variable")
print("with probability parameter pin = %4.2f is less than or equal" % pin)
print("to %1i is %8.6f" % (ix, p))

Output¶

The probability that a discrete geometric random variable
with probability parameter pin = 0.25 is less than or equal
to 3 is 0.683594