Explore the vast range of titles available.

Johnson and Wehrly (1978, Journal of the American Statistical Association73, 602-606) and Wehrly and Johnson (1980, Biometrika67, 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, Biometrics60, 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.

This paper proposes a nonparametric approach to estimating the dependence relationships between circular variables and other circular or linear variables using copulas. The proposed method is based on the use of Bernstein copulas which are a very flexible class of non-parametric copulas which allows for the approximation of any kind of dependence structure, including non symmetric relationships. In particular, we present a simple procedure to adapt Bernstein copulas to the circular framework and guarantee that the constructed bivariate distributions are strictly continuous. We provide two illustrative case studies, the first on the relation between wind direction and quantity of rainfall in the North of Spain and the second on the dependence between the wind directions in two nearby buoys at the Atlantic ocean.

Underdetermined Blind Source Separation (UBSS) refers to a general class of signal processing algorithms, aiming to recover the underlying source signals from related mixtures without resorting to any prior information about the mixing matrix system and with less sensors than source signals. Technologies such as teleconferencing, hands-free telephony and hearing aids mostly require real-time processing. This matter is a major challenge in BSS problem, as traditional methods generally require significant amounts of data to generate sufficient statistics for separation. So, the proposed method is trying to give an overall solution for low latency applications. For this purpose, the High-Resolution Sub-Band Decomposition (HRSBD) algorithm in sparse time domain is utilized to compensate the low data efficiency of short time block lengths. Additionally, in contrast to the conventional methods which presume the known number of source signals during processing frames, we derive an adaptive source counting procedure in each processing block. Some clustering techniques assume a linear distribution for the audio mixture, whereas some others utilize circular statistics. Most of the linear approaches lead to failure in the case of directional data and most of the circular methods are unable to generalize in the case of multi-dimensional setup (multiple-microphone setup). Our research proves that the nature of mixing data in UBSS problem has both linear and circular features. Therefore, a new clustering scheme is proposed which effectively addresses the directional data and multi-dimensional setup simultaneously. Finally, we propose a separation procedure with low computational complexity which selects the best separation method considering the results of adaptive source counting phase of the algorithm. Experimental evaluations show the superiority of the proposed method against the state-of-the-art techniques according to the remarkable and dominant high performance of estimating the number of sources, mixing matrix estimation accuracy and the effective results of the source separation in both instantaneous and reverberant conditions.

The procedure of outliers detection in univariate circular data can be developed using clustering algorithm. In clustering, it is necessary to calculate the similarity measure in order to cluster the observations into their own group. The similarity measure in circular data can be determined by calculating circular distance between each point of angular observation. In this paper, clustering-based procedure for outlier detection in univariate circular biological data with different similarity distance measures will be developed and the performance will be investigated. Three different circular similarity distance measures are used for the outliers detection procedure using single-linkage clustering algorithm. However, there are two similarity measures namely Satari distance and Di distance that are found to have similarity in formula for univariate circular data. The aim of this study is to develop and demonstrate the effectiveness of proposed clustering-based procedure with different similarity distance measure in detecting outliers. Therefore, in this study the circular similarity distance of SL-Satari/Di and another similarity measure namely SL-Chang will be compared at certain cutting rule. It is found that clustering-based procedure using single-linkage algorithm with different similarity distances are applicable and promising approach for outlier detection in univariate circular data, particularly for biological data. The result also found that at a certain condition of data, the SL-Satari/Di distance seems to overperform the performance of SL-Chang distance.

A new one-parameter distribution is proposed for circular data based on wrapping. Most distributions constructed via wrapping do not yield elementary expressions for their mathematical properties. Yet the new distribution yields elementary expressions for all of its mathematical properties. Better fits of the new distribution over the three-parameter distribution due to Jones and Pewsey 10 and six other wrapped distributions including four that have two parameters each are shown for at least two data sets. Better fits were assessed in terms of probability plots, density plots, values of Akaike information criterion and values of Bayesian information criterion.

Statistical inference on the circle may strongly depend on the chosen reference system. Here, we introduce necessary and sufficient conditions to avoid inferential problems and misinterpretation of parameter estimates for any circular distribution. The construction of invariant distributions, with respect to the reference system, is discussed by introducing specific properties. Numerical examples on simulations and data are presented to corroborate and illustrate theoretical results.

Applications of circular regression models appear in many different fields such as evolutionary psychology, motor behavior, biology, and, in particular, in the analysis of gene expressions in oscillatory systems. Specifically, for the gene expression problem, a researcher may be interested in modeling the relationship among the phases of cell-cycle genes in two species with differing periods. This challenging problem reduces to the problem of constructing a piecewise circular regression model and, with this objective in mind, we propose a flexible circular regression model which allows different parameter values depending on sectors along the circle. We give a detailed interpretation of the parameters in the model and provide maximum likelihood estimators. We also provide a model selection procedure based on the concept of generalized degrees of freedom. The model is then applied to the analysis of two different cell-cycle data sets and through these examples we highlight the power of our new methodology.

Data visualization is important for statistical analysis, as it helps convey information efficiently and shed lights on the hidden patterns behind data in a visual context. It is particularly helpful to display circular data in a two-dimensional space to accommodate its nonlinear support space and reveal the underlying circular structure which is otherwise not obvious in one-dimension. In this article, we first formally categorize circular plots into two types, either height- or area-proportional, and then describe a new general methodology that can be used to produce circular plots, particularly in the area-proportional manner, which in our opinion is the more appropriate choice. Formulas are given that are fairly simple yet effective to produce various circular plots, such as smooth density curves, histograms, rose diagrams, dot plots, and plots for multiclass data. Supplemental materials for this article are available online.

Data from camera traps that record the time of day at which photographs are taken are used widely to study daily activity patterns of photographed species. It is often of interest to compare activity patterns, for example, between males and females of a species or between a predator and a prey species. In this article we propose that the similarity between two activity patterns may be quantified by a measure of the extent to which the patterns overlap. Several methods of estimating this overlap measure are described and their comparative performance for activity data is investigated in a simulation study. The methods are illustrated by comparing activity patterns of three sympatric felid species using data from camera traps in Kerinci Seblat National Park, Sumatra.

This paper presents robust estimators for binary and multinomial circular logistic regression, where a circular predictor is related to the response. An extensive Monte Carlo Simulation Study clearly shows the robustness of proposed methods. Finally, three numerical examples of Botany, Crime and Meteorology illustrate the application of these methods to Life and Social Sciences. Although in the Botany data the proposed method showed little improvement, in the Crime and Meteorological data an increment up to 5\\% and 4\\% of accuracy, respectively, is achieved.