src/nmath/pgeom.c (PR#1834)

[ripley@stats.ox.ac.uk]

On 26 Jul 2002, Morten Welinder wrote:

>
>    >     return log(1 - p) * (x + 1);
>    >
>    > looks like it has problems for p near 1.  I would suggest rewriting it to
>
>    Could you give us an example of the problems please?  Otherwise how
>    will we know that we have solved them?
>
> Visual inspection.  The problem is that the original code performs an
> operation, "1-p", with the potential of killing all precision.  Often

But for p near 1 (you give near 0 below) the distribution is concentrated
almost entirely on a single point.

> that cannot be helped, but here the function log1p exists as a counterpart
> to log in order to solve this very problem.
>
>    >     return log1p (-p) * (x + 1);
>
>    Please report the bug (see BUGS in the FAQ) and not the solution.  It
>    seems to me to be working fine for p as small as 10^(-8) which is already
>    way beyond a feasible application of a geometric (as an exponential would
>    be used instead).
>
> It is entirely likely that such values are unreasonable, but that is still
> not a great reason for returning terrible results for something that is at
> least theoretically sane.  The actual point where problems occur is going
> to depend on your floating point hardware.  For me, p=1e-17 makes the old
> version return zero (fundamentally wrong) and the new version non-zero.

That's nowhere near one!

> Note, that variations of "log (1-p)" exist in other functions, such as
> pbeta_raw.

I think this amounts to

`if I were to do really silly things numerical inaccuracies might catch up
with me'.

That's true throughout R, but we do have better things to worry about.

-- 
Brian D. Ripley,                  ripley@stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595


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