A tractable, parsimonious and flexible model for cylindrical data, with applications

Circular–linear data; Circular–linear regression; Distributions on the cylinder; Sine-skewed von Mises distribution; Weibull distribution; Statistics and Probability; Economics and Econometrics; Statistics, Probability and Uncertainty

Abstract :

[en] New cylindrical distributions are proposed by combining the sine-skewed von Mises distribution (circular part) with the Weibull distribution (linear part). This new model, the WeiSSVM, enjoys numerous advantages: simple normalizing constant and hence very tractable density, parameter-parsimony and interpretability, good circular–linear dependence structure, easy random number generation thanks to known marginal/conditional distributions, and flexibility illustrated via excellent fitting abilities. Inferential issues, such as independence testing, circular–linear respectively linear–circular regression, can easily be tackled with the new model, which is applied on two real data sets.

Disciplines :

Mathematics

Author, co-author :

Abe, Toshihiro ; Department of Information Systems and Mathematical Sciences, Nanzan University, Nagoya, Japan

LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Gent, Belgium

External co-authors :

yes

Language :

English

Title :

A tractable, parsimonious and flexible model for cylindrical data, with applications

Publication date :

October 2017

Journal title :

Econometrics and Statistics

ISSN :

2468-0389

eISSN :

2452-3062

Publisher :

Elsevier B.V.

Volume :

Pages :

91 - 104

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S2452306216300168?httpAccept=text/xml

Funding text :

Toshihiro Abe was supported in part by JSPS KAKENHI Grant number 15K17593 and Nanzan University of Pache Research Subsidy I-A-2 for the 2015 academic year. Christophe Ley was supported in part by the Fonds National de la Recherche Scientifique, Communauté française de Belgique, via a Mandat de Chargé de Recherche. Both authors would like to thank three anonymous referees for helpful comments that led to an improvement of the present paper.

Available on ORBilu :

since 25 November 2023

Statistics

Number of views

58 (1 by Unilu)

Number of downloads

13 (0 by Unilu)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Abe, T., Pewsey, A., Sine-skewed circular distributions. Stat. Pap. 52 (2011), 683–707.
Fernández-Durán, J.J., Models for circular–linear and circular–circular data constructed from circular distributions based on nonnegative trigonometric sums. Biometrics 63 (2007), 579–585.
Fisher, N.I., Lee, A.J., Regression models for an angular response. Biometrics 48 (1992), 665–677.
García-Portugués, E., Barros, A.M.G., Crujeiras, R.M., González-Manteiga, W., Pereira, J.M.C., A test for directional-linear independence, with applications to wildfire orientation and size. Stoch. Environ. Res. Risk Assess. 28 (2014), 1261–1275.
García-Portugués, E., Crujeiras, R.M., González-Manteiga, W., Exploring wind direction and SO2 concentration by circular–linear density estimation. Stoch. Environ. Res. Risk Assess. 27 (2013), 1055–1067.
Gradshteyn, I.S., Ryzhik, I.M., Tables of Integrals, Series, and Products, eight ed., 2015, Academic Press, London.
Johnson, R.A., Wehrly, T.E., Measures and models for angular correlation and angular-linear correlation. J. R. Stat. Soc. Ser. B 39 (1977), 222–229.
Johnson, R.A., Wehrly, T.E., Some angular-linear distributions and related regression models. J. Am. Stat. Assoc. 73 (1978), 602–606.
Jones, M.C., Pewsey, A., A family of symmetric distributions on the circle. J. Am. Stat. Assoc. 100 (2005), 1422–1428.
Kato, S., Shimizu, K., Dependent models for observations which include angular ones. J. Stat. Plan. Inference 138 (2008), 3538–3549.
Lagona, F., Picone, M., Model-based segmentation of spatial cylindrical data. J. Stat. Comput. Simul. 86 (2016), 2598–2610.
Lagona, F., Picone, M., Maruotti, A., A hidden Markov model for the analysis of cylindrical time series. Environmetrics 26 (2015), 534–544.
Lagona, F., Picone, M., Maruotti, A., Cosoli, S., A hidden Markov approach to the analysis of space-time environmental data with linear and circular components. Stoch. Envir. Res. Risk Assess. 29 (2015), 397–409.
Maksimov, V.M., Necessary and sufficient statistics for a family of shifts of probability distributions on continuous bicompact groups. Rossiskaya Akademiya Nauk. Teor. Verojatnost. i Primenen. 12 (1967), 307–321 (in Russian). English Translation: Theory of Probability and its Applications 12, 267–280.
Mardia, K.V., Linear-circular correlation coefficients and rhythmometry. Biometrika 63 (1976), 403–405.
Mardia, K.V., Sutton, T.W., A model for cylindrical variables with applications. J. R. Stat. Soc. Ser. B 40 (1978), 229–233.
Pewsey, A., Testing circular symmetry. Can. J. Stat. 30 (2002), 591–600.
Stacy, E.W., A generalization of the Gamma distribution. Ann. Math. Stat. 33 (1962), 1187–1192.
Wang, F., Gelfand, A.E., Jona-Lasinio, G., Joint spatio-temporal analysis of a linear and a directional variable: Space-time modeling of wave heights and wave directions in the Adriatic Sea. Stat. Sin. 25 (2015), 25–39.
Wang, J., Boyer, J., Genton, M.G., A skew-symmetric representation of multivariate distribution. Stat. Sin. 14 (2004), 1259–1270.
Wang, M.-Z., Shimizu, K., Uesu, K., An analysis of earthquakes latitude, longitude and magnitude data by use of directional statistics. Jpn. J. Appl. Stat. 42 (2013), 29–44 (in Japanese).