Your suggestions would not fix the problems.
There many values y which exceeds %:x but
x tcdf y is not theoretically or even practically 1.
For example,
3 tcdf 2.35336
|assertion failure: tcdf
| (%:x)>|y
But (from tables) the value should be 0.95.
Moreover, for any finite y (less than 0 or otherwise),
x tcdf y should mathematically not be 0. e.g.
3 tcdf _1e_30
0.5
So this is a case where y<0 but the mathematical
answer is 0.5, contrary to
> 0 instead of assert when y<0 or when y<0 and the
> calculation is not 0.
----- Original Message -----
From: Robert Cyr <[EMAIL PROTECTED]>
Date: Tuesday, August 12, 2008 18:02
Subject: Re: [Jprogramming] general Gamma distribution
To: Programming forum <[email protected]>
> concerning Roger Hui's formula for the students CDF,
>
> It would be handy to return
>
> 1 instead of assert when y>0 or when y>0 and the calculation
> returns less
> than 0
>
> 0 instead of assert when y<0 or when y<0 and the
> calculation is not 0.
>
> On Tue, Aug 12, 2008 at 8:40 PM, Robert Cyr
> <[EMAIL PROTECTED]> wrote:
>
> > There appears to be a sign problem in the formula.
> >
> > The formula either form Wolfram or wikipedia are:
> >
> > tcdf=: 4 : 0
> > assert. (%:x)>|y
> > 0.5 + y * (!-:x+1) * ((0.5,-:1+x) H. 1.5 x%~-*:y) %
> (%:o.x) * !<:-:x
> > )
> >
> > As noted by others, the limit also needs to be adjusted.
> > The limits probably are too high, as tcdf cannot exceed
> 1. It seems to be
> > in that region that problem results occur.
> >
> >
> > On Tue, Aug 12, 2008 at 5:38 PM, Roger Hui
> <[EMAIL PROTECTED]> wrote:
> >
> >> For large x one may want to use the N(0,1) CDF
> >> in a pinch. From
> >> http://www.jsoftware.com/jwiki/Essays/Normal_CDF
> >>
> >> erf =: (1 H. 1.5)@*: * 2p_0.5&* % ^@:*:
> >> n01cdf=: -: @ >: @ erf @ %&(%:2)
> >>
> >> 10 tcdf 3
> >> 0.993328
> >> n01cdf 3
> >> 0.99865
> >>
> >> The bad 100 tcdf 9 result is likely due to extreme
> >> accumulation of numerical errors. On my machine I get:
> >>
> >> 100 tcdf 9
> >> 1.03437e17
> >>
> >> n01cdf 9
> >> 1
> >> 1 - n01cdf 9
> >> _2.22045e_16
> >>
> >>
> >>
> >> ----- Original Message -----
> >> From: John Randall <[EMAIL PROTECTED]>
> >> Date: Tuesday, August 12, 2008 14:07
> >> Subject: Re: [Jprogramming] general Gamma distribution
> >> To: Programming forum <[email protected]>
> >>
> >> > Roger Hui wrote:
> >> > > It's the absolute value of y that should be bounded,
> >> > > not just y itself. Thus:
> >> > >
> >> > > tcdf=: 4 : 0
> >> > > assert. (%:x)>|y
> >> > > 0.5 + y * (!-:x-1) * ((0.5,-:1+x) H. 1.5 x%~-*:y) %
> >> > (%:o.x) * !<:-:x
> >> > > )
> >> > >
> >> > >
> >> > Mathworld <http://mathworld.wolfram.com/Studentst-
> >> > Distribution.html> has
> >> > different formulations (equations 7 and 8), which
> rely on
> >> > the incomplete
> >> > beta function and are not subject to the hypergeometric bounds.
> >> >
> >> > I don't think the restriction is bad when x (degrees of freedom)
> >> > is above
> >> > about 10. For example
> >> >
> >> > 10 tcdf 3
> >> > 0.993328
> >> >
> >> > but it is not good if x is smaller. High values
> of y
> >> > give strange results:
> >> >
> >> > 100 tcdf 9
> >> > _7.15204e15
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