Hello,
 
I want to fit a distribution to a dataset. Important is not the "overall"
fitting but the fitting in the tail (e.g. all observations > x or the n
highest values). Standard ML-estimation sometimes doesn't work here very
well. We see that especially when we have truncated datasets the algorithms
won't converge. In the case of lognormal distribution: It seems that the
farer the truncation point is away from the peak of the whole distribution
the more unlikely is the convergence.
 
So I think to do the following. And my questions are: Before I try to do it
with basic R-knowledge on my own ... maybe there is a similar solution
already available in R. And:  maybe somebody can give me further reading on
this topic or has other/better ideas how to cope this type of problem
(except EVT-Approaches).
 
First I produce the quantiles for all points of my dataset. I fix that the
fitting will be done for the n largest values. Then an optimization
algorithm starts. The objective function could be a goodness-of-fit
criterion, for a first try e.g: Minimize the sum over all squared deltas
[empirical - theoretical distribution]. In *any* case should be found
parameters that fulfill the condition. The criterion should be able to
overweight observations the higher they are.
 
What do you think about ?
 
Regards, Carsten

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