Recent advances in directional statistics

Abstract

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 (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, aeronautics, 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. We end with an overview of presently available software for analyzing directional data.

Semiparametric inference for mixtures of circular data

“…animal movements), forensics (crime incidence). Different surveys on statistical methods for circular data can be found: Mardia and Jupp (2000), Jammalamadaka and SenGupta (2001), Ley and Verdebout (2017) or more recently Pewsey and García-Portugués (2020). In the present work, we consider a mixture model with two components equal up to a rotation.…”

Comparing the Performance of Navigation Systems Under Complex Environment

“…The fuzzy-based tests can be applied in case of indeterminacy in the data. [11,16,19,23,25,38] and [25] discussed various statistical tests for circular observations under fuzzy logic. More information on the applications of the fuzzy-based analysis can be seen in [1,4] and [5].…”

A New Test for Ridge Wind Directional Data Under Neutrosophic Statistics

“…To deal with such data, the statistical tests using fuzzy logic can be helpful in making a decision about the unknown parameters. (Yang and Pan, 1997), (Chen et al, 2013), (Pewsey et al, 2013), (Kesemen et al, 2016), (Lubiano et al, 2016), (Benjamin et al, 2019) and (Pewsey and García-Portugués, 2020) presented various tests to analyze fuzzy data. (Smarandache, 2014) introduced neutrosophic statistics (NS) to deal with the data having neutrosophic numbers.…”