TheChymera TheChymera - 2 months ago 36
Python Question

Beta Binomial Function in Python

I would like to calculate the probability given by a binomial distribution for predetermined x(successes), n(trials), and p(probability) - the later of which is given by a probability mass function Beta(a,b).

I am aware of

scipy.stats.binom.pmf(x,n,p)
- but I am unsure how I can replace p with a probability function. I am also wondering whether I could use the
loc
argument of
scipy.stats.binom.pmf
to emulate this behaviour.

Answer

Wiki says that the compound distribution function is given by

f(k|n,a,b) = comb(n,k) * B(k+a, n-k+b) / B(a,b)

where B is the beta function, a and b are the original Beta parameters and n is the Binomial one. k here is your x and p disappears because you integrate over the values of p to obtain this (convolution). That is, you won't find it in scipy but it is a one-liner provided you have the beta function from scipy.