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DECENTERED DIRECTIONAL DATA

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BERNARD BOULERICE AND GILLES R. DUCHARME

*Département de mathématiques et statistique, Université de Montréal,*

C. P. 6128, Succ. A, Montréal, Québec, Canada H3C 3J7
(Received March 29, 1993; revised September 28, 1993)

**Abstract.**
Directional data analysis usually
assumes that the observations are recorded according to a
coordinate system whose origin coincides with the center of
their support. However, it may happen that the observer does
not sit at this center and record the directions from
another point. The object of this paper is to investigate
the statistical behavior of such decentered directions.
First we derive the family of distributions of these
directions and produce statistical procedures that recover
some information about the underlying process. An important
special case is explored in details and compared with the
Langevin model. Finally, an example is given where the
introduced family of models makes physical sense and well
fits the observations.

*Key words and phrases*:
Directional data,
goodness-of-fit, group family,
Langevin distribution,
location shift, maximum likelihood theory, rotational
symmetry, uniform distribution, von Mises Fisher
distribution.

**Source**
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