[issue36018] Add a Normal Distribution class to the statistics module

[Mark Dickinson]

Mark Dickinson <dickinsm at gmail.com> added the comment:

Below is the full transcript from Pari/GP: note that I converted the float inputs to exact Decimal equivalents, assuming IEEE 754 binary64. Summary: both Python results look fine; it's Nspire that's inaccurate here.


mirzakhani:~ mdickinson$ /opt/local/bin/gp
                                            GP/PARI CALCULATOR Version 2.11.1 (released)
                                    i386 running darwin (x86-64/GMP-6.1.2 kernel) 64-bit version
                               compiled: Jan 24 2019, Apple LLVM version 10.0.0 (clang-1000.11.45.5)
                                                      threading engine: single
                                           (readline v8.0 enabled, extended help enabled)

                                               Copyright (C) 2000-2018 The PARI Group

PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER.

Type ? for help, \q to quit.
Type ?17 for how to get moral (and possibly technical) support.

parisize = 8000000, primelimit = 500000
? \p 200
   realprecision = 211 significant digits (200 digits displayed)
? ncdf(x, mu, sig) = (2 - erfc((x - mu) / sig / sqrt(2))) / 2
%1 = (x,mu,sig)->(2-erfc((x-mu)/sig/sqrt(2)))/2
? ncdf(5.37399999999999966604491419275291264057159423828125, 2, 1.3000000000000000444089209850062616169452667236328125)
%2 = 0.99527574392076815760565921436860970675961162900034485433923192853608778325191325235412640687571628164064779657215907190523884572141701976336760387216713270956350229484865180142256611330976179584951493
? ncdf(-0.2300000000000000099920072216264088638126850128173828125, 2, 1.3000000000000000444089209850062616169452667236328125)
%3 = 0.043137367078910025352120502108682523151629166877357644882244088336773338416883044522024586619860574718679715351558322591944140762629090301623352497457372937783778706411712862062109829239761761597057063

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<https://bugs.python.org/issue36018>
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