[R] find parameters for a gamma distribution

[Prof Brian Ripley]

On Wed, 5 Jan 2005, Prof Brian Ripley wrote:

> First, you want to fit the data not the histogram counts (binned data).
>
> Second, glm does not do a very principled fit of a gamma (it is a moment 
> estimator).  Something like
>
>> d <- rgamma(1000, 20, scale = 2)
>> summary(glm(d ~ 1, Gamma))
> Coefficients:
>             Estimate Std. Error t value Pr(>|t|)
> (Intercept) 0.0253072  0.0001822   138.9   <2e-16
>
> (Dispersion parameter for Gamma family taken to be 0.05185392)
>
> where the shape = 1/0.05185392 (no s.e.) and 0.0253072 is the mean
> = 1/(scale*shape)

[In case it confuses you, that got garbled in a cut-and-paste:

0.0253072 is the rate = 1/mean = 1/(scale*shape) as the default link for 
the Gamma glm is reciprocal.

]

>
> Try instead (on 100000 obs here)
>
> library(MASS)
> fitdistr(d, "Gamma")
>      shape           rate
>  19.812444027    0.495157589
> ( 0.087858938) ( 0.002223778)
>
> which works for me.  You can make it use scale =1/rate by
>> fitdistr(d, dgamma, start=list(shape=20,scale=2))
>      shape          scale
>  19.812702659    2.019419771
> ( 0.087774433) ( 0.009060263)
>
>
> On Wed, 5 Jan 2005, Andrew Collier wrote:
>
>> hello,
>> 
>> i have just started exploring R as an alternative to matlab for data 
>> analysis. so
>> +far everything is _very_ promising. i have a question though regarding 
>> parameter
>> +estimation. i have some data which, from a histogram plot, appears to 
>> arise from
>> +a gamma distribution. i gather that you can fit the data to the 
>> distribution
>> +using glm(). i am just not quite sure how this is done in practice... so 
>> here is
>> +a simple example with artificial data:
>> 
>> d <- rgamma(100000, 20, scale = 2)
>> h <- hist(d, breaks = c(seq(10, 80, 2), 100))
>> 
>> H <- data.frame(x = h$mids, y = h$density)
>> 
>> g <- glm(y ~ x, data = H, family = Gamma)
>> summary(g)
>> 
>> Call:
>> glm(formula = y ~ x, family = Gamma, data = H)
>> 
>> Deviance Residuals:
>>    Min       1Q   Median       3Q      Max
>> -3.8654  -2.0887  -0.7685   0.7147   1.4508
>> 
>> Coefficients:
>>            Estimate Std. Error t value Pr(>|t|)
>> (Intercept)  30.4758    26.7258   1.140    0.262
>> x             1.0394     0.6825   1.523    0.137
>> 
>> (Dispersion parameter for Gamma family taken to be 1.343021)
>> 
>>    Null deviance: 119.51  on 35  degrees of freedom
>> Residual deviance: 116.28  on 34  degrees of freedom
>> AIC: -260.49
>> 
>> Number of Fisher Scoring iterations: 7
>> 
>> now i suppose that the estimates parameters are:
>> 
>>        shape = 30.4758
>>        scale = 1.0394
>> 
>> am i interpreting the output correctly? and, if so, why are these estimates 
>> so
>> +poor? i would, perhaps naively, expected the parameters from an artificial
>> +sample like this to be pretty good.
>> 
>> my apologies if i am doing something stupid here but my statistics 
>> capabilties
>> +are rather limited!
>> 
>> best regards,
>> andrew collier.
>> -- 
>> Andrew B. Collier
>> 
>> Antarctic Research Fellow                                   tel: +27 31 
>> 2601157
>> Space Physics Research Institute                            fax: +27 31 
>> 2616550
>> University of KwaZulu-Natal, Durban, 4041, South Africa
>> 
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide! 
>> http://www.R-project.org/posting-guide.html
>> 
>
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595
>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595