(50g) Normal Distribution

[Albert Chan]

(12-08-2018 07:13 PM)John Keith Wrote:  ... the idea of using 1-ln(sqrt(2*pi)) proved to be less accurate on the HP 50 so I stuck with dividing by sqrt(2*pi) instead.

For 12-digits calculator, this constant is better, relative error ~ 1.25e-18

k = e^-0.88453 / √(2 Pi) = 0.164726 536723 000000 206 ... => 0.164726 536723

Z(x) = exp(0.88453 - B) exp(B - I²/2 - I F - F²/2) * k

Examples:

Z(20.33333 33333) = exp(0.88453 - 413/2) exp(-0.222222 221544) * 0.164726 536723 = 6.64644 887123 e-91

Z(16.4285 714286) = exp(0.88453 - 269/2) exp(-0.448979 592306) * 0.164726 536723 = 9.84720 298683 e-60

edit: 1 - ln(sqrt(2*pi)) constant had a flaw I missed. exp(-1-B) term might underflow to 0.0