How to use Monte Carlo simulation to obtain propotion confidence interval for Bernoulli events with unequal probabilities?
Probably this question is not so related to Matlab itself, however, I know many talented mathematicians are here and I hope I can get some helps from you guys. I am doing some work to calculate the confidence interval for a Poisson-binomial distribution. This distribution has been rarely mentioned even by professional statisticians. Suppose N independent Bernoulli trials exist and two results exist for each trial: “pass” or ”fail”. Now K of N trials have been observed as “pass”. If an identical “pass” probability is applied to all trials, K will follow a well-studied Binomial distribution. If different “pass” probabilities are applied, K will follow a rarely known Poisson-binomial distribution. Obviously, Binomial distribution is a special but simple version of Poisson-binomial distribution. Now I have obtained a K value from a set of N independent Bernoulli trials with unequal “pass” probabilities (assume these probabilities are pre-known). As defined above, I know K will follo
