>>Hi,
>>
>>How can I fit a t-distribution to a sample?
>From my point of view this is not purely an S-Plus question.
Perhaps the estimation technique most often used to fit a t-distribution is the
maximum likelihood
method.
However it can happen (quite often if the d.f. is small) that the ML-estimate
is not unique assuming
t-distributed errors.
Perhaps the following papers may be interesting.
E.g.
EM-algorithm
\item[] {\rm Lange, K.L., Little, R.J.A. and Taylor, J.M.G.} (1989).
Robust statistical modelling using the t distribution.
{\em J. Amer. Statist. Assoc.}, {\bf 84}, 881-886.
\item[] {\rm M{\"a}kel{\"a}inen, T., Schmidt, K. \& Styan, G.P.H.} (1981).
On the existence and uniqueness of the maximum likelihood estimate of a
vector-valued parameter in fixed-size samples.
{\em Ann. Statist.}, {\bf 9}, 758-767.
\item[] {\rm Copas, J.B.} (1975).
On the unimodality of the likelihood for the Cauchy distribution.
{\em Biometrika}, {\bf 62}, 701-704.
\item[] {\rm Barnett, V.} (1966).
Evaluation of the maximum-likelihood estimator where the
likelihood equation has multiple roots.
{\em Biometrika}, {\bf 53}, 151-165.
\item[] {\rm Kent, J.T. and Tyler, D.E.} (1991).
Redescending M-estimates of multivariate location and scatter.
{\em Ann. Statist.}, {\bf 19}, 2102-2119.
%- Key words:
%- redescending M-estimate
%- robustness
%- multivariate t-distribution
Yours sincerely,
Andreas
----------------------------------------------
A.Christmann@hrz.uni-dortmund.de
PD Dr. Andreas Christmann
Universitaet Dortmund
Hochschulrechenzentrum
Wissenschaftliche Anwendungen
D-44221 Dortmund
GERMANY
phone (049)-231-755-2763
fax -2731
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