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Question about Poisson Binomial Distribution #14

Open peanubnutter opened 1 year ago

peanubnutter commented 1 year ago

Hi Deak,

I couldn't figure out another way to contact you. I have a few questions about the Poisson Binomial Distribution you wrote about here. I've found it really invaluable - it's the only accessible article on this topic I've found on the internet, and I've searched for a weeks.

In the Scala code for the Refined Normal Approximation I have two points of confusion: 1) G is constructed using the CDF of the standard normal distribution, so is G also a CDF? 2) If G is a CDF, then what does the prob() function represent? Is it actually cumulativeProbability (probability of x <= k not x = k)? 3) Why does the pmf() function use the rna() function (rescaling by mu/sigma) for each possible value of k, but prob() uses g() directly, not rescaling when computing for an input k?

peanubnutter commented 1 year ago

I think the definition of G(x) is mistaken, where the /6 should apply to only the second (skewness) term, not the entire right hand side. It would make sense to me that the second term is a correction to the normal CDF, so the normal CDF shouldn't be divided.