The ihygecdf function calculates the inverse hypergeometric cumulative distribution (CDF).

Synopsis

ihygecdf(cumulative_probability, successes, failures, trials)

Summary

The inverse hypergeometric cumulative distribution function returns the maximum number of expected successful events, given the following parameters:

cumulative_probability – the cumulative probability of the event occurring
successes – the total number of possible successes
failures – the total number of possible failures
trials – the number of times the experiment is repeated without replacement

Example

In a batch of 100 marbles, 20 marbles are white and 80 are black. Find the probability of drawing between 0 and x white marbles in a batch of 10 randomly selected marbles using the hypergeometric CDF.

Create a matrix to hold the number of successes (x):

AFL% store(build(<success:double>[x=0:9], double(x)), success_array);

Apply the cumulative probability of x or fewer successes computed using the direct hypergeometric CDF, and store in prob_array:

AFL% store(apply(success_array, prob, hygecdf(success,20,80,10)), prob_array);

The output is:

{x} success,prob
{0} 0,0.0951163
{1} 1,0.363049
{2} 2,0.68122
{3} 3,0.890428
{4} 4,0.974535
{5} 5,0.996067
{6} 6,0.999608
{7} 7,0.999976
{8} 8,0.999999
{9} 9,1

Apply the inverse hypergeometric CDF to the probabilities in prob_array:

AFL% apply(prob_array, inverse, ihygecdf(prob,20,80,10));

The output is:

{x} success,prob,inverse
{0} 0,0.0951163,0
{1} 1,0.363049,1
{2} 2,0.68122,2
{3} 3,0.890428,3
{4} 4,0.974535,4
{5} 5,0.996067,5
{6} 6,0.999608,6
{7} 7,0.999976,7
{8} 8,0.999999,8
{9} 9,1,9

Remove the example arrays:

AFL% remove(success_array); remove(prob_array);

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