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calcACProbabilityCI - calculate confidence interval for the probability

function calcACProbabilityCI(p, times, alpha);

The function is used to calculate the Agresti-Coull confidence interval for probability estimate p obtained in times trials. Argument alpha indicates the desired significance level.

calcACProbabilityCI returns two numbers: the beginning and end of the confidence interval.

Values of alpha other then 0.05, 0.01, 0.001 are not supported and would lead to empty confidence interval around p.

A simple case:

-- Let the random variable x has the following values;
x = {1.35, 1.34, 1.37, 1.36, 1.35, 1.40, 1.35, 1.37, 1.32, 1.34};

-- The probability of x > 1.34 can be estimated like that;
p = 0.0;
for i = 1, #x do
   if x[i] > 1.34 then p = p + 1.0 end
   end

p = p / #x; -- 0.7

-- To get the desired confidence interval simply call the function;
pMin, pMax = calcACProbabilityCI(p, #x, 0.05); -- 0.392, 0.897

Confidence interval for the probability