[R] Goodness of fit for gamma distributions

[Albyn Jones]

it is easy to make a qqplot for the gamma; suppose that the sample parameters
are 1.101 and 2.49, the data in x:

          plot(qgamma(ppoints(x),1.101,2.49),sort(x))

see also lattice:qqmath

albyn

Quoting Dan31415 <d.m.mitchell at reading.ac.uk>:

>
> Ah yes, that does produce a nice plot. Can i just ask what exactly it is
> showing. It seems to me to be a sort of Q-Q plot but with a different set of
> axes. Is this correct, if so do the same interpretation rules apply for this
> plot, i.e. departures from either end of the curve show poor fitting of the
> extreme data.
>
> thanks for your help Remko, its been very helpful.
>
> Dann
>
>
>
> Remko Duursma-2 wrote:
>>
>> It sounds like you just want to graph it though. For gammas, it's nice
>> to graph the log of the density, because
>> the tail is so thin and long, so you don't see much otherwise:
>>
>> mydata <- rgamma(10000, shape=1.1, rate=2.5)
>>
>> # now suppose you fit a gamma distribution, and get these estimated
>> parameters:
>> shapeest <- 1.101
>> rateest <- 2.49
>>
>> h <- hist(mydata, breaks=50, plot=FALSE)
>> plot(h$mids, log(h$density))
>> curve(log(dgamma(x, shape=shapeest, rate=rateest)), add=TRUE)
>>
>>
>> #Remko
>>
>>
>> -------------------------------------------------
>> Remko Duursma
>> Post-Doctoral Fellow
>>
>> Centre for Plant and Food Science
>> University of Western Sydney
>> Hawkesbury Campus
>> Richmond NSW 2753
>>
>> Dept of Biological Science
>> Macquarie University
>> North Ryde NSW 2109
>> Australia
>>
>> Mobile: +61 (0)422 096908
>>
>>
>>
>> On Wed, Jan 28, 2009 at 1:13 AM, Dan31415 <d.m.mitchell at reading.ac.uk>
>> wrote:
>>>
>>> Thanks for that Remko, but im slightly confused because isnt this testing
>>> the
>>> goodness of fit of 2 slightly different gamma distributions, not of how
>>> well
>>> a gamma distribution is representing the data.
>>>
>>> e.g.
>>>
>>> data.vec<-as.vector(data)
>>>
>>> (do some mle to find the parameters of a gamma distribution for data.vec)
>>>
>>> xrarea<-seq(-2,9,0.05)
>>> yrarea<-dgamma(xrarea,shape=7.9862,rate=2.6621)
>>>
>>> so now yrarea is the gamma distribution and i want to compare it with
>>> data.vec to see how well it fits.
>>>
>>> regards,
>>> Dann
>>>
>>>
>>> Remko Duursma-2 wrote:
>>>>
>>>> Hi Dann,
>>>>
>>>> there is probably a better way to do this, but this works anyway:
>>>>
>>>> # your data
>>>> gamdat <- rgamma(10000, shape=1, rate=0.5)
>>>>
>>>> # comparison to gamma:
>>>> gamsam <- rgamma(10000, shape=1, rate=0.6)
>>>>
>>>> qqplot(gamsam,gamdat)
>>>> abline(0,1)
>>>>
>>>>
>>>> greetings
>>>> Remko
>>>>
>>>>
>>>> -------------------------------------------------
>>>> Remko Duursma
>>>> Post-Doctoral Fellow
>>>>
>>>> Centre for Plant and Food Science
>>>> University of Western Sydney
>>>> Hawkesbury Campus
>>>> Richmond NSW 2753
>>>>
>>>> Dept of Biological Science
>>>> Macquarie University
>>>> North Ryde NSW 2109
>>>> Australia
>>>>
>>>> Mobile: +61 (0)422 096908
>>>>
>>>>
>>>>
>>>> On Tue, Jan 27, 2009 at 3:38 AM, Dan31415 <d.m.mitchell at reading.ac.uk>
>>>> wrote:
>>>>>
>>>>> I'm looking for goodness of fit tests for gamma distributions with
>>>>> large
>>>>> data
>>>>> sizes. I have a matrix with around 10,000 data values in it and i have
>>>>> fitted a gamma distribution over a histogram of the data.
>>>>>
>>>>> The problem is testing how well that distribution fits. Chi-squared
>>>>> seems
>>>>> to
>>>>> be used more for discrete distributions and kolmogorov-smirnov seems
>>>>> that
>>>>> large sample sizes make it had to evaluate the D statistic. Also i
>>>>> haven't
>>>>> found a qq plot for gamma, although i think this might be an
>>>>> appropriate
>>>>> test.
>>>>>
>>>>> in summary
>>>>> -is there a gamma goodness of fit test that doesnt depend on the sample
>>>>> size?
>>>>> -is there a way of using qqplot for gamma distributions, if so how
>>>>> would
>>>>> you
>>>>> calculate it from a matrix of data values?
>>>>>
>>>>> regards,
>>>>> Dann
>>>>> --
>>>>> View this message in context:
>>>>> http://www.nabble.com/Goodness-of-fit-for-gamma-distributions-tp21668711p21668711.html
>>>>> Sent from the R help mailing list archive at Nabble.com.
>>>>>
>>>>> ______________________________________________
>>>>> R-help at r-project.org mailing list
>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>>> PLEASE do read the posting guide
>>>>> http://www.R-project.org/posting-guide.html
>>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>>
>>>>
>>>> ______________________________________________
>>>> R-help at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>
>>>>
>>>
>>> --
>>> View this message in context:
>>> http://www.nabble.com/Goodness-of-fit-for-gamma-distributions-tp21668711p21686095.html
>>> Sent from the R help mailing list archive at Nabble.com.
>>>
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>
> --
> View this message in context:  
> http://www.nabble.com/Goodness-of-fit-for-gamma-distributions-tp21668711p21725468.html
> Sent from the R help mailing list archive at Nabble.com.
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>