Recently I was using SciPy’s `scipy.stats.binom.pmf(x,n,p)`

. I though it would be great if I could have such a function in q. So a simple idea is to construct a binomial tree with probabilities attached. Recalling that a Pascal triangle is generated using `n{0+':x,0}1`

, I modified it to get:

q)pmf:{[n;p]n{(0,y*1-x)+x*y,0}[p]/1#1f} q)pmf[6;0.3] 0.000729 0.010206 0.059535 0.18522 0.324135 0.302526 0.117649 q)sum pmf[1000;0.3] 1f

What is great about this method is that it is stable. Compared to SciPy 0.7.0, it was more accurate too (it is a known issue that older SciPy has buggy binom.pmf):

>>> scipy.stats.binom.pmf(range(0,41),40,0.3)[-5:] >>> array([3.33066907e-15, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00, 1.11022302e-16]) q)-5#pmf[40;0.7] 3.293487e-15 1.52594e-16 5.162955e-18 1.134715e-19 1.215767e-21

Unfortunately this method is too slow for large n. For large n, we need more sophisticated methods. For the interested reader, take a look at Catherine Loader’s Fast and Accurate Computation of Binomial Probabilities paper and an implementation of a binomial distribution in…

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