# [R] Problem with reproducing log likelihood estimated with ghyp package

peter dalgaard pdalgd at gmail.com
Sun Dec 18 10:53:42 CET 2011

```On Dec 17, 2011, at 10:57 , Steinar wrote:

> I was playing around with the ghyp package and simulated series of
> t-distributed variables when suddenly i was not able to reproduce the log
> likelihood values reported by the package. When trying to reproduce the
> likelihood values, I summed the log(dt(x,v)) values and it worked with some
> simulated series but not all.
>
> Is there any obvious flaws with this script?

Try rethinking your definition of the likelihood.

I would expect that the likelihood depends on the scale and position parameters via (x-mu)/sigma or so. As far as I can tell, you are de facto setting mu=0 and sigma=1, which might sort of work if you are simulating with mu=0 and sigma=1, but not when sigma=5.

> library("ghyp")
> series_1=rt(10000,4)
>
> #simulating 10000 relation of student t variables with df=4
> #Which implies a standrad deviation equal to sqrt(2)
>
> series_2=series_1/sqrt(2)*5
>
> #To get student t distributed variabler with standard
> #deviation equal to 5 I rescale the first series
>
> #When i check the first series with the ghyp package, the result coincides
> with
> #the sum of log likelihood calculated with dt(x, df, ncp, log = FALSE)
>
> fit_1=fit.tuv(series_1, silent=T, symmetric=T)
> fit_1
> sum(log(dt(series_1,coef(fit_1)\$nu,0)))
>
> #The two log likelihood estimates is approximatly equal, and the parameters
> are
> #sensible.
>
> #When I check series 2, i get a very different result. The estimate for mu
> and nu
> #is still sensible, but the log likelihood is very different from what i get
> with
> #dt(x, df, ncp, log = FALSE)
>
> fit_2=fit.tuv(series_2, silent=T, symmetric=T)
> fit_2
> sum(log(dt(series_2,coef(fit_2)\$nu,0)))
>
> #This is very different
>
>
>
> --
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>
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