[R] implementing Maximum Likelihood with distrMod when only the PDF is known

[guillaume.martin]

Dear Mathias,
That's pretty amazing, thanks a lot ! I'll have to look all this through 
because I don't easily understand why each part has to be set up, in 
particular the "initialize method" part seems crucial and is not easy to 
intuit. From what I get, the actual name we give to a parameter (my 
original "mu" for example) is important in itself, and if we introduce 
new variable names we have to define a new generic, right? The simplest 
option then is to re-use an existing variable name that has the same 
properties/range, right?

Another general question: my actual pdf is of the same type but not the 
exact same as the skew normal. In particular, I don't have a rule for 
building the slot r (eg the one borrowed from the sn package in your 
example); is it a problem? isn't it sufficient to give slot d, and then 
you have automatic methods implemented to get from d() to r() slots etc. 
is that right?

Thanks a lot for your help and time !

Best,

Guillaume


Matthias Kohl a écrit :
> Dear Guillaume,
>
> thanks for your interest in the distrMod package.
>
> Regarding your question I took up your example and put a file under:
>
> http://www.stamats.de/distrModExample.R
>
> Hope that helps ...
>
> Don't hesitate to contact me if you have further questions!
>
> Best,
> Matthias
>
> guillaume.martin schrieb:
>> Dear R users and Dear authors of the distr package and sequels
>>
>> I am trying to use the (very nice) package distrMod as I want to 
>> implement maximum likelihood (ML) fit of some univariate data for 
>> which I have derived a theoretical continuous density (pdf). As it is 
>> a parametric density, I guess that I should implement myself a new 
>> distribution of class AbscontDistributions (as stated in the pdf on 
>> "creating new distributions in distr"), and then use MLEstimator() 
>> from the distrMod package. Is that correct or is there a simpler way 
>> to go? Note that I want to use the distr package because it allows me 
>> to implement simply the convolution of my theoretical pdf with some 
>> noise distribution that I want to model in the data, this is more 
>> difficult with fitdistr or mle.
>> It proved rather difficult for me to implement the new class 
>> following all the steps provided in the example, so I am asking if 
>> someone has an example of code he wrote to implement a parametric 
>> distribution from its pdf alone and then used it with MLEstimator().
>>
>> I am sorry for the post is a bit long but it is a complicate question 
>> to me and I am not at all skillful in the handling of such notions as 
>> "S4 - class", etc.. so I am a bit lost here..
>>
>> As a simple example, suppose my theoretical pdf is the skew normal 
>> distribution (available in package sn):
>>
>> #skew normal pdf (default values = the standard normal N(0,1)
>>
>> fsn<-function(x,mu=0,sd=1,d=0) {u = (x-mu)/sd;  f = 
>> dnorm(u)*pnorm(d*u); return(f/sd)}
>>
>> # d = shape parameter (any real), mu = location (any real), sd = 
>> scale (positive real)
>>
>> #to see what it looks like try
>> x<-seq(-1,4,length=200);plot(fsn(x,d=3),type="l")
>>
>> #Now I tried to create the classes "SkewNorm" and "SkewNormParameter" 
>> copying the example for the binomial
>> ##Class:parameters
>> setClass("SkewNormParameter",
>> representation=representation(mu="numeric",sd="numeric",d="numeric"),
>> prototype=prototype(mu=0,sd=1,d=0,name=gettext("Parameter of the Skew 
>> Normal distribution")),
>> contains="Parameter"
>> )
>>
>> ##Class: distribution (created using the pdf of the skew normal 
>> defined above)
>> setClass("SkewNorm",prototype = prototype(
>>     d = function(x, log = FALSE){fsn(x, mu=0, sd=1,d=0)},
>>     param = new("SkewNormParameter"),
>>     .logExact = TRUE,.lowerExact = TRUE),
>> contains = "AbscontDistribution"
>> )
>>
>> #so far so good but then with
>> setMethod("mu", "SkewNormParameter", function(object) object at mu)
>>
>> #I get the following error message:
>>
>> > Error in setMethod("mu", "SkewNormParameter", function(object) 
>> object at mu) : no existing definition for function "mu"
>>
>> I don't understand because to me mu is a parameter not a function... 
>> maybe that is too complex programming for me and I should switch to 
>> implementing my likelihood by hand with numerical convolutions and 
>> optim() etc., but I would like to know how to use distr, so if there 
>> is anyone who had the same problem and solved it, I would be very 
>> grateful for the hint !
>>
>> All the best,
>> Guillaume
>>
>>
>>
>

-- 
Guillaume MARTIN
Institut des Sciences de l'Evolution de Montpellier
ISEM UMR 5554, Bât. 22 Université Montpellier II
34 090 Montpellier, France

tel: (+33) 4 67 14 32 50