I hope this is the way to send a request for help, but a former colleague who
works in a European Research Institute in Italy passed this query to me in
the week.
Please reply to:
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I have a problem in which I can easily compute the null hypothesis moments of
a test
statistic. To find a good approximation for setting the test threshold, I am
studying the different methods for fitting a distribution given the moments.
The only things I know about are, the Pearson curves and the Johnson method
as they are described in Kendall and Stuart (Volume 1,1963, Chapter 6,
"Standard Distribution-2". Of course, I noticed in the translation of the
Neuilly book, that you have a section on fitting of Pearson distributions
which I enjoyed reading. I have also read what is to be found in G.J. Hahn
and S.S. Shapiro, Statistical Models in Engineering (Chapter 6, Approximation
by Empirical Distributions), Wiley 1967.
I am hoping to have a student here next year who will make a simulation
comparison of approximation methods as a work for an MSc thesis. In preparing
myself for this, I am hoping that maybe you might have a more up-to-date
knowledge of the literature on this subject than I do, and hence I am hoping
that maybe you can point me in the direction of any other approaches (
perhaps recently developed) other than the classical methods of Pearson and
Johnson and that you could perhaps suggest to me any more recent books which
treat the subject in good pedagogic detail (even if only for Pearson and
Johnson/with student in mind).
Many thanks,
Derek Pike
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