R help - Aug 2012 - finding the MLEs of IG parameters by EM-Alorithm

Dear all

I'm trying to caculate the MLEs for parameters of Inverse Gaussian
distribution (in a k-sample problem with common mean) by using
EM-Algorithm.  I found some package for EM-Algorithm that are useful
for missing or incomplete data and are not helpful for solving my
problem.
(Exactly, the problem is: Let Xij, i=1,..,k , j=1,...,ni, be a random
sample from IG(?,?i). So the log-likelihood function is:
log(L)=?(ni/2)*log(?i)-?? (?i/2*(?^2)*xij)*((xij-?)^2)+const.
Find the MLEs for (?,?1,...,?k) by EM-Algorithm?)

Could you please help me with that?
I would like to thank you in advance for your help.

best regards,
Sara

On Aug 2, 2012, at 16:01 , Sara S wrote:
> Dear all
> 
> I'm trying to caculate the MLEs for parameters of Inverse Gaussian
> distribution (in a k-sample problem with common mean) by using
> EM-Algorithm.  I found some package for EM-Algorithm that are useful
> for missing or incomplete data and are not helpful for solving my
> problem.
> (Exactly, the problem is: Let Xij, i=1,..,k , j=1,...,ni, be a random
> sample from IG(?,?i). So the log-likelihood function is:
> log(L)=?(ni/2)*log(?i)-?? (?i/2*(?^2)*xij)*((xij-?)^2)+const.
> Find the MLEs for (?,?1,...,?k) by EM-Algorithm?)
> 
> Could you please help me with that?
No. Its a theory problem, not an R one. You likely need to rephrase the problem
as a missing-data problem. I don't see how, but the text containing the
exercise may contain a hint somewhere in the vicinity.
> I would like to thank you in advance for your help.
> 
> best regards,
> Sara
-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com