A new multimodal and asymmetric bivariate circular distribution

Hassanzadeh, Fatemeh; Kalaylıoğlu, Zeynep

doi:10.1007/s10651-018-0409-3

Cited by 3 publications

(2 citation statements)

References 31 publications

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“…Its one-dimensional conditional distributions are GvM 2 , and the sine multivariate vM model is a special case of it. Hassanzadeh and Kalaylioglu (2018) recently proposed a model for data on T 2 obtained using a conditional specification construction involving GvM 2 pdfs.…”

Section: Models For Toroidal Datamentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

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Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

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Section: Models For Toroidal Datamentioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

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“…More recently, Navarro et al (2017) conditioned a multivariate normal distribution to obtain the twelve-parameter bivariate generalized von Mises model of order 2 (BGvM 2 ), whose conditional distributions are second-order generalized von Mises (GvM 2 ), see, for example, Gatto (2008), while Hassanzadeh and Kalaylioglu (2018) used a conditional specification approach to obtain a toroidal model with one of its marginal distributions being GvM 2 . GvM 2 densities can be symmetric or asymmetric and unimodal or bimodal.…”

Section: Introductionmentioning

confidence: 99%

Tractable circula densities from Fourier series

Kato

Pewsey

Jones

2021

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This article proposes an approach, based on infinite Fourier series, to constructing tractable densities for the bivariate circular analogues of copulas recently coined ‘circulas’. As examples of the general approach, we consider circula densities generated by various patterns of nonzero Fourier coefficients. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. The special cases of the circula densities we consider all have simple closed-form expressions involving no computationally demanding normalizing constants and display wide-ranging distributional shapes. A highly successful model identification tool and methods for parameter estimation and goodness-of-fit testing are provided for the circula densities themselves and the bivariate circular densities obtained from them using a marginal specification construction. The modelling capabilities of such bivariate circular densities are compared with those of five existing models in a numerical experiment, and their application illustrated in an analysis of wind directions.

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