[WP34s] Regularized incomplete Beta function

[Dieter]

(05-07-2014 12:12 AM)Paul Dale Wrote:  I understand now.
We'll stick with CNVG? 00.

I now tend to think the accuracy limit is not in the quantile code but in the Student CDF itself (resp. in the probably underlying Incomplete Beta function). Comparing some results with the 34s t_u function showed the well-known pattern:

Code:


t=1, dof=5
true:  0.1816087338245613128000742599987684
WP34s: 0.1816087338245613128000742599987684   = 34 correct digits

t=2, dof=5
true:  0.05096973941492917812268055292114372
WP34s: 0.05096973941492917812268055292114375  = 33 correct digits

t=1, dof=20
true:  0.1646282885858545321288508309266107
WP34s: 0.1646282885858545321288508309266112   = 32 correct digits

t=2, dof=20
true:  0.02963276772328523648480977051479628
WP34s: 0.02963276772328523648480977051479624  = 33 correct digits

t=2, dof=100
true:  0.02410608936556683980047800955979969
WP34s: 0.02410608936556683980047800955980203  = 31 correct digits

t=2, dof=300
true:  0.02320076049157454520121192249335514
WP34s: 0.02320076049157454520121192249334880  = 31 correct digits

t=1, dof=2000
true:  0.1587157390503716353822190042123339
WP34s: 0.1587157390503716353822190042125858   = 30 correct digits

t=2, dof=2000
true:  0.02281763665584740680547795791001989
WP34s: 0.02281763665584740680547795791000417  = 30 correct digits

t=1, dof = 20000
true:  0.1586613031239535484612795731910335
WP34s: 0.1586613031239535484612795731911468   = 30 correct digits

This pattern is consistent with information on the accuracy of the one or other Incomplete Beta algorithm included in mathematical software libraries. As a rule of thumb the number of potentially inaccurate digits seems to match the number of digits in the degrees of freedom.

Which leads to the question if an upper limit in the dof value would make sense. For instance a maximum of 1000. This would apply to the Student as well as the Chi² and F distribution.

Dieter