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(12C Platinum) Normal Distribution
12-01-2018, 07:44 PM (This post was last modified: 12-01-2018 07:50 PM by Dieter.)
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RE: (12C Platinum) Normal Distribution
(12-01-2018 05:37 PM)Albert Chan Wrote:  Using x = 0 to 5 step 0.01, confirmed your claim of 1.2e-6 max rel. error ...

With exact coefficents it's even a tad less, about 1,10 E–6.
I like that it's "exact by design" for x=0. ;-)

(12-01-2018 05:37 PM)Albert Chan Wrote:  Nice!

It gets even nicer: take a look at this thread in the HP67 software forum. This implements a (4;5) rational approximation.

Finally, here is the CF expansion that complements the above rational approximation for x>5:

Q(x) ≈ Z(x) / (x+1/(x+2/(x+3/(x+0,66))))

The two largest errors are at x=5 (–1,04 E–6) and x=6,13 (+8,9 E–7). For larger x the error decreases continuously towards zero. At the underflow limit (x=21,16517934) it is merely 1,4 E–9. If exactly evaluated, that is. Which is not possible with the standard 12C implementation of Z(x). The linked HP67/97 program evaluates the PDF differently to achieve better accuracy.

Dieter
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(12C Platinum) Normal Distribution - Gamo - 12-01-2018, 07:53 AM
RE: (12C Platinum) Normal Distribution - Dieter - 12-01-2018 07:44 PM



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