On 13/11/2016 1:43 PM, Alexey Burnakov wrote:
Dear R-Devel group,
My name is Alexey, a data scientist from Moscow, currently working for
Align Technology Inc.
We have recently had a discussion of the results that the dgamma
function (stats) returns for an extreme point (x == 0).
<dgamma(0,1,1,log = FALSE)
[1] 1
and
<dgamma(0,0.5,1,log = FALSE)
[1] Inf
Density appears to be defined in point zero for the distribution with
the said parameters.
It looks like the returned value is a limit of f(x) where x --> inf.
It's the limit as x --> 0.
Although several other "big" statistics engines like Wolfram and Matlab
return 0 (zero) for gamma density with the same function parameters
where x == 0. Which looks like a convention rather than exact answer, in
our opinion. Is this a correct assumption?
When studies scrupulously, it appears that the density is undefined when
we get x^0 where x == 0, for example.
As I could not have reached the author of the code for dgamma, could you
comment on this behavior of the dgamma function in zero? Is it safe to
use the function given such behaviour. Is it prudent to report density =
inf in zero? Is there a preferable way to estimate the gamma density in
zero otherwise?
Using the limit is the most sensible method. Having a discontinuity in
the density will cause more problems, e.g. if the density is used in
quadrature.
As to the "correctness", we all know that the value of a density at any
particular point is irrelevant. Only the integrals of densities have
any meaning.
Duncan Murdoch
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