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An introduction to statistical methods for circular data

87

more recently, Pewsey

et al.

(2013).

Figure 1:

Polar area diagram, by Florence Nightingale (1858). Image

from Wikimedia Commons.

Circular data can be viewed as a particular case of spherical or

directional data (data whose support is a hypersphere of arbitrary

dimension, Mardia (1972)). Hence, methods for spherical data

analysis can be adapted to the unit circle. But sometimes this

up–bottom focus does not take advantage of the simpler nature of

a circle, where data points can be written in polar coordinates and

are still easy to handle. In that respect, Fisher (1993) classifies

circular data somewhere between linear and spherical. On the one

hand, the connection between spherical and circular data has been

already noticed. And on the other hand, there may be argued that

there are not many differences between circular and linear analysis.

If data are concentrated in a part of an arc, then a linearization

argument may seem enough to directly apply linear methods, or

even a periodicity argument could be used to extend periodically