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.

Very Simply Explicitly Invertible Approximations of Normal Cumulative and Normal Quantile Function

SORANZO, Alessandro;
2014-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2809524
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