Accurate Normal Distribution for the HP67/97

[Dieter]

(12-03-2018 08:25 PM)Albert Chan Wrote:  4th order x correction = t + x/2 · t² + (2x²+1)/6 · t³ + x*(6x²+7)/24 t⁴

Thank you very much. I just found an older VBA function in the Excel sheet where the initial approxmation for the Normal quantile was tested:

Code:

x = x + t * t * t * t * (6 * x ^ 3 + 7 * x) / 24 + t * t * t * (2 * x * x + 1) / 6 + t * t * x / 2 + t
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But I can't say how or when I got to that conclusion. ;-)

With four terms even a not too exciting four-digit approximation like Hastings' yields 15 digit double precision accuracy with just one correction step. Probably even more -- but Excel is limited to these 15 digits.

Dieter