I am looking for an approximation for Poisson binomial distribution:
The Poisson binomial distribution is the discrete probability distribution of a sum of $n$ independent Bernoulli trials. you can find its pdf in http://en.wikipedia.org/wiki/Poisson_binomial_distribution
In addition, you can find 2 methods for it in the mentioned link. But when I use the second method (using Fourier Transform), the result would be an imaginary number.
I also wanted to use approximations in the following paper http://statistics.stanford.edu/~ckirby/techreports/ONR/SOL%20ONR%20467.pdf
but the approximations are not clear to me. I would be grateful if somebody explains to me:
1) why do I get imaginary number using the second method ( Fourier transform)?
2) and also for example, how are the probabilities in Table 2 in the paper calculated?