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Models for Circular–Linear and Circular–Circular Data Constructed from Circular Distributions Based on Nonnegative Trigonometric Sums
Author(s) -
FernándezDurán J. J.
Publication year - 2007
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2006.00716.x
Subject(s) - mathematics , von mises distribution , distribution (mathematics) , skewness , circular buffer , joint probability distribution , random variable , mathematical analysis , geometry , statistics , finite element method , physics , computer science , thermodynamics , programming language , von mises yield criterion
Summary Johnson and Wehrly (1978, Journal of the American Statistical Association 73, 602–606) and Wehrly and Johnson (1980, Biometrika 67, 255–256) show one way to construct the joint distribution of a circular and a linear random variable, or the joint distribution of a pair of circular random variables from their marginal distributions and the density of a circular random variable, which in this article is referred to as joining circular density. To construct flexible models, it is necessary that the joining circular density be able to present multimodality and/or skewness in order to model different dependence patterns. Fernández‐Durán (2004, Biometrics 60, 499–503) constructed circular distributions based on nonnegative trigonometric sums that can present multimodality and/or skewness. Furthermore, they can be conveniently used as a model for circular–linear or circular–circular joint distributions. In the current work, joint distributions for circular–linear and circular–circular data constructed from circular distributions based on nonnegative trigonometric sums are presented and applied to two data sets, one for circular–linear data related to the air pollution patterns in Mexico City and the other for circular–circular data related to the pair of dihedral angles between consecutive amino acids in a protein.