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 <[EMAIL PROTECTED]> 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
~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907
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