R help - Aug 2011 - Gamma distribution parameter estimation

Hey,
I have a set of income data which I'd like to fit to a gamma 
distribution. How can I estimate the two parameters of the gamma 
distribution for a vector, e.g.

c(2039L, 2088L, 5966L, 2353L, 1966L, 2312L, 3305L, 2013L, 3376L,
3363L, 3567L, 4798L, 2032L, 1699L, 3001L, 2329L, 3944L, 2568L,
1699L, 4545L)

I sense this will be a very easy one-liner, but my searching didn't come 
up with results yet.

Thanks in advance,
  Alex

Hi Alex,

Try
> require(MASS)
Loading required package: MASS
> b <- c(2039L, 2088L, 5966L, 2353L, 1966L, 2312L, 3305L, 2013L, 3376L,
+ 3363L, 3567L, 4798L, 2032L, 1699L, 3001L, 2329L, 3944L, 2568L,
+ 1699L, 4545L)
> fitdistr(b, 'gamma')
      shape           rate
  6.4528939045   0.0021887943
 (0.7722567310) (0.0001854559)

HTH,
Jorge


On Sat, Aug 6, 2011 at 3:14 PM, Alexander Engelhardt <> wrote:
> Hey,
> I have a set of income data which I'd like to fit to a gamma
distribution.
> How can I estimate the two parameters of the gamma distribution for a
> vector, e.g.
>
> c(2039L, 2088L, 5966L, 2353L, 1966L, 2312L, 3305L, 2013L, 3376L,
> 3363L, 3567L, 4798L, 2032L, 1699L, 3001L, 2329L, 3944L, 2568L,
> 1699L, 4545L)
>
> I sense this will be a very easy one-liner, but my searching didn't
come up
> with results yet.
>
> Thanks in advance,
>  Alex
>
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> and provide commented, minimal, self-contained, reproducible code.
>
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On 2011-08-06 15:14, Alexander Engelhardt wrote:
> Hey,
> I have a set of income data which I'd like to fit to a gamma
> distribution. How can I estimate the two parameters of the gamma
> distribution for a vector, e.g.
>
> c(2039L, 2088L, 5966L, 2353L, 1966L, 2312L, 3305L, 2013L, 3376L,
> 3363L, 3567L, 4798L, 2032L, 1699L, 3001L, 2329L, 3944L, 2568L,
> 1699L, 4545L)
>
> I sense this will be a very easy one-liner, but my searching didn't
come
> up with results yet.
>
> Thanks in advance,
>   Alex
Straightforward, using the method of L-moments:

   x <- c(2039L, 2088L, 5966L, 2353L, 1966L, 2312L, 3305L, 2013L, 3376L,
          3363L, 3567L, 4798L, 2032L, 1699L, 3001L, 2329L, 3944L, 2568L,
          1699L, 4545L)

   library(lmom)
   (pargam <- pelgam(samlmu(x)))  # Parameter estimates

   evplot(x, quagam, pargam)  # check goodness of fit

Note that allowing the distribution to have a nonzero lower bound,
by fitting a 3-parameter gamma distribution ("Pearson type III" in
the terminology of package lmom), gives a visually much better fit:

   evdistq(quape3, pelpe3(samlmu(x)), col='blue')


J. R. M. Hosking