WP34s: statistical distributions (reminder)

[Dieter]

Since the 34s project recently got some nice improvements and fixes, maybe it's time to humbly remind of an older thread from last May/June where some flaws in the Student CDF – function "t(x)" – and the Student/Chi² quantile functions have been discussed: cf. this thread.

The fix for t(x) is quite simple and straightforward, so that it could be applied immediately (cf. post #9 in the old thread). To see the problem, try t(1E–17) with 10 degrees of freedom: the current firmware returns a plain 0.5 while the exact result is 0.50000 00000 00000 00389 10838 39660 31050 61705..., i.e. there are just 17 valid digits. That's fine for SP, but not for DP. And it also affects the quantile function.

Last year I proposed an improved algorithm for the Student and Chi² quantiles (as well as a slightly modified Normal quantile so that all three distributions share the same Normal estimate). These versions converge well and return good results even in border cases where the current firmware gives up ("No root found"), e.g. at the Student quantile for 1E–1080 and 1000 degrees of freedom. Pauli: if you're still interested I could offer a wp34s.dat file for the emulator with all relevant code, so that you can easily try and test these algorithms. They are based on what was discussed in last year's thread.

Dieter

Edit: typo corrected