[HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL

01012024, 07:56 AM
(This post was last modified: 01022024 05:04 AM by LdBeth.)
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[HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL
There are seven functions of the type % > % provided, they are ERF
function, Q function, and their inverse implemented using numerical approximation methods. Internally they are all computed using extended float. ERF, IERF Implementation of error function and its inverse using method from Sergei Winitzki's paper. ERFIV Implementation of inverse error function using method from Mike Giles' paper. QNORM, IQNORM Implementation of Q function and its inverse using `ERF` and `IERF`. Note the `UPTN` function actually gives a more acurrate result for Q function, but the inverse Q function is much faster than computing the inverse of Q using numerical solver, while the accuracy of both methods are approximately the same. QBEST A slightly better Q function approximation from [Dao Ngoc Phong et al]. If you ask me the result is still not as good as `UPTN`. IQSML This function from Pingyi Fan's paper gives decent approximation to inverse Q function when the input is small enough, and can compute the inverse when `IQNORM` gives infinity error. Reference [Sergei Winitzki] A handy approximation for the error function and its inverse, February 6, 2008. [Dao Ngoc Phong, Nguyen Xuan Hoai, R.I. (Bob) McKay] Evolving the Best Known Approximation to the Q Function. [Mike Giles] Approximating the erfinv function. [Pingyi Fan] New inequalities of Mill's ratio and Its Application to The Inverse Qfunction Approximation erflib.zip (Size: 64.55 KB / Downloads: 5) 

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Messages In This Thread 
[HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL  LdBeth  01012024 07:56 AM
RE: [HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL  Gil  01012024, 08:09 PM
RE: [HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL  LdBeth  01022024, 04:36 AM
RE: [HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL  Gil  01022024, 12:41 PM
RE: [HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL  LdBeth  01032024, 10:42 AM
RE: [HP49/50g] ERF, ERF inverse, Q, Q inverse in SysRPL  Gil  01032024, 02:52 PM

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