[Gretl-users] pvalues [was menu restructuring]
On Wed, 12 Jul 2006, Talha Yalta wrote:
3- Finally, I would like to submit my testing of the p-value
finder in gretl in terms of numerical accuracy. Looks like
gretl has some problems with calculating the correct values
for the left tails for several distributions. Some may find
the inaccuracies insignificant. Still, it might be worth to
take a look into it. The results are attached as a ods
spreadsheet.
Thanks for your rigorous testing.
I have now fixed the code for p-values against the t
distribution: the gretl results agree exactly with ELV.
As for the Chi-square and F results, there's a basic problem
here, to do with finite-precision computer arithmetic. In
principle, if you calculate
P1 = Prob(X <= X0) and
P2 = Prob(X >= X0)
then you should have P1 = 1 - P2. But that's not the case with
double-precision numbers, or not for all values of X0.
For instance, you had some cases with very small X0. The
"p-value" quoted by gretl is P2, and in many cases it equals
"1.0". However, if you use the underlying cephes engine to
calculate P1, you get a (very small) positive answer that agrees
precisely with ELV. (But if you then try finding 1 - P1 you get
1.0 again!)
The trouble is that doubles do not model the real line, and the
set of representable doubles is denser close to zero than it is
just short of 1. That is, there are numbers D such that D
does not equal 0.0 but 1 - D = 1.
I've fixed this, to an extent, for the "pvalue" command. You'll
now see this sort of thing:
? pvalue X 50 0.999
Chi-square(50): area to the right of 0.999 = 1
(to the left: 1.15939e-33)
I'm not sure how to handle it for the pvalue() function in genr
-- maybe there could be some option to return the left-tail
value rather than the right. Perhaps if you enter a negative x
you get the left value?
Allin.