[R] many zeroes in rgamma ... what's going on?

[Peter Dalgaard]

Prof Brian Ripley wrote:
> On Sun, 18 Nov 2007, Gregory Gentlemen wrote:
>
>> Dear Dr. Dalgaard,
>>
>> Thank you for your insight! In fact, I did read the example
>> documentation, however, it pretty much told me the same thing that my
>> little simulation did: there is ALOT of point mass at zero.
>>
>> Is there any fix to this problem? Seeing that rgamma won't work
>> accurately, if I wanted to plot a density of an inverse gamma
>> distribution with small scale and shape parameters, how would I do so?
>
> You haven't understood the issue snown in the example.  This is not about
> 'won't work accurately', but 'can't work accurately':  half the mass
> is on numbers which cannot be represented in your computer.
>
> and Vincent Goulet wrote
>
>> Package actuar has the {d,p,q,r}invgamma() functions (and quite a few
>> others), if this can be of any help to you.
>
> But it cannot, because the reciprocals cannot be represented either
> (and actually the issue is a little worse because there is no gradual
> overflow).  And indeed that is what happens if you try the suggestion.
>
>

Yes. What I think you can do is a little pencil-and-paper work to find
out the density of Y=log(X). The main issue is that the density for X
for small x is effectively proportional to x^(a-1) which becomes
uncomfortably close to the unintegrable x^(-1) when a is small. A change
of variable involves dy=dx/x, which cancels the near-singularity.


>> Peter Dalgaard <p.dalgaard at biostat.ku.dk> wrote: Gregory Gentlemen
>> wrote:
>>> Hello fellow R users,
>>>
>>> I wanted to view the density on the standard deviation scale of a
>>> gamma(0.001, 0.001) prior for the precision. I did this as seen in
>>> the code below and found that for some reason rgamma is giving many
>>> values equal to zero, which is strange since a gamma distribution is
>>> continuous. What is going on here?
>>>
>>> Thanks for any help in advance.
>>> Greg
>>>
>> That sort of shape parameter gives a distribution with most of its mass
>> squashed against the y axis, so random numbers underflow to zero. But
>> why did you not read the Example section of help(rgamma)? The effect is
>> clearly indicated there.
>>
>>>
>>>> x1 <- rgamma(10000, shape=0.001, scale=0.001)
>>>> sd1 <- 1/sqrt(x1)
>>>> truehist(sd1, xlim=c(0, 1.5))
>>>>
>>> Error in truehist(sd1, xlim = c(0, 1.5)) :
>>>         'nbins' must result in a positive integer
>>>
>>>> summary(sd1)
>>>>
>>>       Min.    1st Qu.     Median       Mean    3rd Qu.       Max.
>>>  2.266e+01  9.311e+66 3.250e+153        Inf        Inf        Inf
>
>


-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907