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EnglishFor the normal cumulative distribution function: Φ(x) we give the new approximation 2**(-22**(1-41**(x/10))) for any x>0, which is very simple (with only integer constants and operations - and / and power elevation **) and is very simply explicitly invertible having 1 entry of x. It has 3 decimals of precision having absolute error less than 0.00013. We compute the inverse which approximates the normal quantile function, or probit, and it has the relative precision of 1 percent (from 0.5) till beyond 0.999. We give an open problem and a noticeable bibliography. We report several other approximations.
| Titolo: | Very Simply Explicitly Invertible Approximations of Normal Cumulative and Normal Quantile Function |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Abstract: | For the normal cumulative distribution function: Φ(x) we give the new approximation 2**(-22**(1-41**(x/10))) for any x>0, which is very simple (with only integer constants and operations - and / and power elevation **) and is very simply explicitly invertible having 1 entry of x. It has 3 decimals of precision having absolute error less than 0.00013. We compute the inverse which approximates the normal quantile function, or probit, and it has the relative precision of 1 percent (from 0.5) till beyond 0.999. We give an open problem and a noticeable bibliography. We report several other approximations. |
| Handle: | http://hdl.handle.net/11368/2809524 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.12988/ams.2014.45338 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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