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. 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? Regards, Alexey Burnakov
dgamma density values in extreme point
2 messages · Alexey Burnakov, Duncan Murdoch
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