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88

R. M. Crujeiras

the data from [0

,

2

π

) to the real line. This work will be mainly

focused on the specific case of circular data, without attempting to

give a general view on the spherical case. For that purpose, the

reader is referred to Mardia and Jupp (2000) and the forthcoming

volume by Ley and Verdebout (2017), with un updated overview on

modern directional statistics. So, it seems that finding a balance

between both perspectives may be a good option: imitate methods

from linear data, adapted and accounting for the circular nature but

in a way that their extension may facilitate the construction of more

sophisticated tools for spherical data.

The goal of this paper is to introduce in a simple way some

methods for circular data analysis, without aiming to be exhaustive,

and showing the potential use of R (R Core Team, 2016) packages

to perform such analysis. Pewsey

et al.

(2013) is indeed an

invaluable contribution for this purpose. The authors present a

thorough an detailed review on circular statistics with R, focusing

on the use of package

circular

. There are also other packages such

isocirc

(Barrag´an

et al.

, 2013),

CircNNTS

(Fern´andez-Dur´an and

Gregorio-Dom´ınguez, 2016) or

movMF

. The recently released package

Directional

also includes some specific functions for circular data.

A special attention will be placed in

NPCirc

(Oliveira

et al.

, 2014),

focused on the use of smoothing methods for circular density and

regression.

This paper is organized as follows. Section 2 is focused on

circular densities, presenting some parametric models and density

estimation procedures. Circular variables are analyzed in a different

role in Section 3, as explanatory and/or response variables in a

regression model. Other modelling and inference problems are briefly

mentioned in Section 4, jointly with some comments on available

software for analyzing circular data.