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Suppose I flip a coin 584,369 times and observe 5,257 heads and 579,112 tails. I wish to know the lower edge of the 90% credible interval for the probability that the next flip will come up heads.

I believe:

I installed SciPy, and wrote:

from scipy.special import betainc, beta

numer = betainc(5257, 579112, 0.05)
denom = beta(5257, 579112)

print numer
print denom
print numer / denom

I get

1.0
0.0
./foo.py:6: RuntimeWarning: divide by zero encountered in double_scalars
  print numer / denom
inf

That is not what I want. I believe this web page calculator says I want 0.008793824176376785502, which is plausible (close to 5257/(5257+579112)=0.00899602819451).

So: are my beliefs correct? How do I calculate this lower edge in Python?

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Friend of mine answered this: I want the inverse cumulative distribution, i.e. the place on the X axis where the cumulative distribution is at 0.05.

In SciPy, the easiest thing is btdtri.

print btdtri(5257, 579112, 0.05)

gives

0.0087938241764
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