[R] The gamma function and infinity
Martin Maechler
maechler at stat.math.ethz.ch
Mon Dec 5 17:51:56 CET 2005
>>>>> "PD" == Peter Dalgaard <p.dalgaard at biostat.ku.dk>
>>>>> on 05 Dec 2005 17:14:47 +0100 writes:
PD> Florent Bresson <f_bresson at yahoo.fr> writes:
>> I have to calculate some formula like:
>>
>> gamma(x)/(gamma(x+y)
>>
>> and I observed that for relatively big values of x, R
>> returns infinity and so cannot compute the formula. Is it
>> possible to force R to give the real value of gamma(x)
>> instead of Inf ?
PD> No, it is overflowing the floating point representation.
PD> How about using lgamma? That's basically what it is for.
Indeed. Note however that in the case of really large x and
moderate y, even in the lgamma() formulation, there will be loss
of precision due to cancellation. There are "famous" asymptotic
(non-convergent series) formulae, you can use in that case, the
most simple one being
Gamma(a + y) / Gamma(a) ~ a^y (for a -> Inf, y << a)
and hence
log(Gamma(a + y)) - log(Gamma(a)) ~ y*ln(a)
--
Martin Maechler, ETH Zurich
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