betas_area.py

from math import lgamma
from numba import jit

@jit
def h(a, b, c, d):
    num = lgamma(a + c) + lgamma(b + d) + lgamma(a + b) + lgamma(c + d)
    den = lgamma(a) + lgamma(b) + lgamma(c) + lgamma(d) + lgamma(a + b + c + d)

    return np.exp(num - den)

@jit
def g0(a, b, c):    
    return np.exp(lgamma(a + b) + lgamma(a + c) - (lgamma(a + b + c) + lgamma(a)))

@jit
def hiter(a, b, c, d):
    while d > 1:
        d -= 1
        yield h(a, b, c, d) / d

def g(a, b, c, d):
    return g0(a, b, c) + sum(hiter(a, b, c, d))

def calc_area_between(beta1, beta2):
    return g(beta1.args[0], beta1.args[1], beta2.args[0], beta2.args[1])

calc_area_between(beta_T, beta_C)