Very simply explicitly invertible approximations of normal cumulative and normal quantile function
Alessandro Soranzo, Emanuela Epure · Applied Mathematical Sciences · 2014
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.