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haskell / math-functions

Special mathematical functions
http://hackage.haskell.org/package/math-functions
BSD 2-Clause "Simplified" License
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Loss of precision in incomplete beta when x=p/(p+q) #36

Closed Shimuuar closed 8 years ago

Shimuuar commented 8 years ago

There's discontinuity when switching between two areas for x, Here is plot for incompleteBeta 4.5 4.5

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This of course adversely affects precision of inverse incomplete beta in area.

Shimuuar commented 8 years ago

Plot for \a → incompleteBeta a a (0.5+δ) - incompleteBeta a a (0.5-δ). E.g. gap size

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Note sudden drop to 0 at a=10

Shimuuar commented 8 years ago

Turns out is due to loss of precision in logBeta for p < 10 && q < 10. It uses logGamma which isn't very precise but itself. Replacing logGamma with logGammaL in otherwise branch of logBeta fixed problem.

Shimuuar commented 8 years ago

Partially fixed in b4819949e5016f3cbcdc88d25556531b5c839a64 by switching to Lanczos approximation everywhere.

Shimuuar commented 8 years ago

b4819949e5016f3cbcdc88d25556531b5c839a64 markedly improved precision of gamma function for z<1, so I think it's safe to mark this as fixed.