def gdir_pdf_integ(self, alpha1, alpha2, alpha3):
from math import gamma
from operator import mul
alpha = np.array([alpha1, alpha2, alpha3])
coef1 = gamma(np.sum(alpha)) / reduce(mul, [gamma(a) for a in alpha])
coef2 = reduce(mul, [xx ** (aa - 1)
for (xx, aa) in zip(self.x, alpha)])
coef3 = reduce(mul, [self.gamma_dist.pdf(local) for local in alpha])
return coef1 * coef2 * coef3
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