Abstract
We consider problems of inference for the wrapped skew-normal distribution on the circle. A centered parametrization of the distribution is introduced, and simulation used to compare the performance of method of moments and maximum likelihood estimation for its parameters. Maximum likelihood estimation is shown, in general, to be superior. The operating characteristics of two moment based tests, for wrapped normal and wrapped half-normal parent populations, respectively, are also explored. The former test is easy to apply, maintains the nominal significance level well and is generally highly powerful. The latter test does not hold the nominal significance level so well, although it is very powerful against negatively skew alternatives. Likelihood based tests for the two distributions are also discussed. A real data set from the ornithological literature is used to illustrate the application of the developed methodology and its extension to finite mixture modelling.
Similar content being viewed by others
References
A Azzalini (1985) ArticleTitleA class of distributions which includes the normal ones Scand J Stat. 12 171–178
A Azzalini A. Capitanio (1999) ArticleTitleStatistical applications of the multivariate skew-normal distribution J Royal Stat Soc Ser B. 61 579–602 Occurrence Handle10.1111/1467-9868.00194
E. Batschelet (1981) Circular statistics in biology Academic Press London
B Bruderer L. Jenni (1990) Migration across the Alps E. Gwinner (Eds) Bird migration: physiology and ecophysiology. Springer-Verlag Berlin 60–77
NI. Fisher (1993) Statistical analysis of circular data Cambridge University Press Cambridge
N. Henze (1986) ArticleTitleA probabilistic representation of the ‘skew-normal’ distribution Scand J Stat. 13 271–275
SR Jammalamadaka A SenGupta (2001) Topics in circular statistics World Scientific Singapore
KV. Mardia (1972) Statistics of directional data Academic Press London
KV Mardia PE. Jupp (1999) Directional statistics Wiley Chichester
AI. McLeod (1985) ArticleTitleA remark on AS 183 An efficient and portable pseudo-random number generator Appl Stat. 34 198–200 Occurrence Handle10.2307/2347378
JA Nelder R Mead (1965) ArticleTitleA simplex method for function minimization Comput J. 7 308–313
R. O’Neill (1971) ArticleTitleAlgorithm AS 47: function minimization using a simplex procedure Appl Stat. 20 338–345 Occurrence Handle10.2307/2346772
A. Pewsey (2000a) ArticleTitleThe wrapped skew-normal distribution on the circle Commun Stat – Theory Meth. 29 2459–2472
A Pewsey (2000b) ArticleTitleProblems of inference for Azzalini’s skew-normal distribution J Appl Stat. 27 859–870 Occurrence Handle10.1080/02664760050120542
A. Pewsey (2004) ArticleTitleThe large-sample joint distribution of key circular statistics Metrika 60 25–32 Occurrence Handle10.1007/s001840300294
BA Wichmann ID Hill (1982) ArticleTitleAlgorithm AS 183: an efficient and portable pseudo-random number generator Appl Stat 31 188–190 Occurrence Handle10.2307/2347988
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: September 2003/ Revised: April 2005
Rights and permissions
About this article
Cite this article
Pewsey, A. Modelling asymmetrically distributed circular data using the wrapped skew-normal distribution. Environ Ecol Stat 13, 257–269 (2006). https://doi.org/10.1007/s10651-005-0010-4
Issue Date:
DOI: https://doi.org/10.1007/s10651-005-0010-4