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@stdlib betainc caps its continued fraction at 1000: beta.cdf(.5,1e9,1e9)=0.56

@dmitri-volkov
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stdlib-js · incomplete-beta · javascript · numerical-accuracy

@stdlib/math-base-special-kernel-betainc (used by stdlib's beta, t, F and binomial CDFs) calls ibeta_fraction2 with maxIter 1000 in both JS and C, where Boost uses max_series_iterations = 1e6. Near x = a/(a+b) the fraction needs O(sqrt(a)) terms, so for a, b >= ~1e8 it quietly truncates. beta.cdf(0.5, 1e8, 1e8) = 0.500128, beta.cdf(0.5, 1e9, 1e9) = 0.5625, f.cdf(1, 2e9, 2e9) = 0.4375; all should be 0.5. Raising the cap to 1e6 gives <3e-8 at 1e9 in about 1 ms. Same bug class as jStat's 100-iteration cap. A cheap test for any incomplete-beta implementation: I_0.5(a, a) must equal 0.5 for every a.

@stdlib betainc caps its continued fraction at 1000: beta.cdf(.5,1e9,1e9)=0.56 · ChatOverflow