The igeomcdf function calculates the inverse geometric cumulative distribution function (CDF).

Synopsis

igeomcdf(x,p)

Summary

The inverse geometric CDF returns the smallest positive integer x such that the geometric CDF evaluated for cumulative probability p is equal to or greater than x.

Example

Given the value of the inverse geometric function, and the probability of getting a particular number from the roll of a fair die (1/6), calculate the smallest number of failures – rolling anything but a 6 for example – before rolling a success – a 6 in this case.

Create a 5-by-5 matrix to hold the cumulative probabilities:
```
AFL% CREATE ARRAY probabilities<prob:double>[i=0:4; j=0:4];
```
Put numerical values of 1/26 to 25/26 into the cells of the matrix:
```
AFL% store(build(probabilities, (i*5+j+1)/26.0), probabilities);
```

Apply the igeomcdf function to the values in the attribute prob:

AFL% apply(probabilities, result, igeomcdf(prob, 0.1667));

The output is:

{i,j} prob,result
{0,0} 0.0384615,0
{0,1} 0.0769231,0
{0,2} 0.115385,0
{0,3} 0.153846,0
{0,4} 0.192308,1
{1,0} 0.230769,1
{1,1} 0.269231,1
{1,2} 0.307692,2
{1,3} 0.346154,2
{1,4} 0.384615,2
{2,0} 0.423077,3
{2,1} 0.461538,3
{2,2} 0.5,3
{2,3} 0.538462,4
{2,4} 0.576923,4
{3,0} 0.615385,5
{3,1} 0.653846,5
{3,2} 0.692308,6
{3,3} 0.730769,7
{3,4} 0.769231,8
{4,0} 0.807692,9
{4,1} 0.846154,10
{4,2} 0.884615,11
{4,3} 0.923077,14
{4,4} 0.961538,17

So, for example, there is a 96.1538% chance that you will roll 17 or fewer non-6s before rolling a 6.

Remove the example array:
```
AFL% remove(probabilities);
```