The ibinomcdf function calculates the inverse binomial cumulative distribution function (CDF).

Synopsis

ibinomcdf(obs_prob,trials,success_prob)

Summary

The inverse binomial CDF returns the smallest number x such that the binomial CDF evaluated at x is equal to or greater than obs_prob for number of trials trials with probability success_prob.

Example

This example creates an array with the binomial CDF for tossing a fair coin 10 times, and then calculates the inverse binomial CDF to demonstrate that the result matches the original values. (For a fair coin, the probability of heads on any given toss is 0.5.)

Create a 1-by-11 array called coin_toss:

AFL% CREATE ARRAY coin_toss<heads:double>[i=0:10];
AFL% store(build(coin_toss, double(i)), coin_toss);

The output is:

{i} heads
{0} 0
{1} 1
{2} 2
{3} 3
{4} 4
{5} 5
{6} 6
{7} 7
{8} 8
{9} 9
{10} 10

Apply the direct binomcdf function to the values in the attribute heads and store the result in the cumulative_prob array:

AFL% store(apply(coin_toss, direct, binomcdf(heads, 10.0, 0.5)), cumulative_prob);

The output is:

{i} heads,direct
{0} 0,0.000976562
{1} 1,0.0107422
{2} 2,0.0546875
{3} 3,0.171875
{4} 4,0.376953
{5} 5,0.623047
{6} 6,0.828125
{7} 7,0.945312
{8} 8,0.989258
{9} 9,0.999023
{10} 10,1

Apply ibinomcdf to the direct probability values the cumulative_prob array:

AFL% apply(cumulative_prob, inverse, ibinomcdf(direct, 10.0, 0.5));

The output is:

{i} heads,direct,inverse
{0} 0,0.000976562,0
{1} 1,0.0107422,1
{2} 2,0.0546875,2
{3} 3,0.171875,3
{4} 4,0.376953,4
{5} 5,0.623047,5
{6} 6,0.828125,6
{7} 7,0.945312,7
{8} 8,0.989258,8
{9} 9,0.999023,9
{10} 10,1,10

Note that the inverse attribute's probabilities match the number of heads from the original coin_toss array.

Remove the example arrays:

AFL% remove(coin_toss); remove(cumulative_prob);