[WP-34S] Chi-Square Distribution

[Dieter]

(01-12-2014 09:38 PM)Paul Dale Wrote:  Turning trace mode on lets you single step through xrom.
...
Yeah, the initial guess is bad for some input values:
...
Seems good for larger values and really small ones. Pretty bad at .05 however.

Seems we found the first error. Take a look at the initial estimates for 0,05 and 0,95. They are the same. In the center, the guess is based on the Normal estimate, so that I assume there might be a problem there. You may want to check if the Normal estimate returns the same absolute value with opposite signs for 0,05 and 0,95.

Back then we discussed different possible ways to provide a good estimate for the Chi^2 quantile. So the version I tried yesterday may be different from the one that actually got implemented. But anyway, here are the results from a slightly simplified method and df=20:

Code:

  p        quantile     estimate
1E-10      0,94544      0,905...
 0,05      10,8508      10,93...
 0,95      31,4104      31,21...
 0,99999   59,0446      58,46...

Not bad for a first estimate, I think. SP accuracy usually does not need more than four or maybe five iterations. If (!) the guess is implemented correctly.

Dieter