Search

The choice of bandwidth is crucial in circular kernel density estimation. Various bandwidth selection techniques have been proposed in the literature. New bandwidth selectors based on the measure β -divergence for kernel density estimation with circular data are presented in this work. These selectors are obtained by minimizing the mean of the measure β -divergence between the density to be estimated and its estimator. The idea is based on the generalization of the standard method which selects the bandwidth by minimizing the mean integrated squared error (MISE). The performance of the proposed selectors is evaluated through a simulation study and compared with other existing selectors. These selectors are illustrated with some real datasets. [ABSTRACT FROM AUTHOR]

Latent factor models are widely used in the social and behavioural sciences as scaling tools to map discrete multivariate outcomes into low-dimensional, continuous scales. In political science, dynamic versions of classical factor models have been widely used to study the evolution of justices' preferences in multi-judge courts. In this paper, we discuss a new dynamic factor model that relies on a latent circular space that can accommodate voting behaviours in which justices commonly understood to be on opposite ends of the ideological spectrum vote together on a substantial number of otherwise closely divided opinions. We apply this model to data on nonunanimous decisions made by the US Supreme Court between 1937 and 2021, and show that for most of this period, voting patterns can be better described by a circular latent space. [ABSTRACT FROM AUTHOR]

The von Mises distribution has played a central role as a distribution on the circle. Its associated circular regression model has been applied in a number of areas. In this paper, we consider the von Mises regression model and, under a sequence of Pitman alternatives, derive the nonnull asymptotic expansions of the cumulative distribution functions of the likelihood ratio, Wald, Rao score, and gradient test statistics for testing a subset of the von Mises regression parameters, as well as for testing the concentration parameter. We then compare analytically the local power of these likelihood-based tests on the basis of the asymptotic expansions and provide conditions where one test can be more locally powerful than the other one in this class of regression models. Consequently, on the basis of the general conditions established, the user can choose the most powerful test to make inferences on the model parameters. We also provide a numerical example to illustrate the usefulness and applicability of the general result. [ABSTRACT FROM AUTHOR]

For the Parzen–Rosenblatt type density estimator for circular data, we prove the existence of a minimizer, h MISE (f ; K , n) , of its exact mean integrated squared error (MISE) and show that it is asymptotically equivalent to the bandwidth h AMISE (f ; K , n) that minimizes the leading terms of the MISE, together with the order of convergence of the relative error h AMISE (f ; K , n) / h MISE (f ; K , n) − 1. Some small and moderate sample size comparisons between the two bandwidths are also presented when the underlying density is a mixture of von Mises densities. [ABSTRACT FROM AUTHOR]

We derive and evaluate a novel estimation approach for the von Mises regression model based on a modified score function whose solution ensures an estimator with a smaller asymptotic bias than the original maximum likelihood estimator. We consider Monte Carlo simulation experiments to show that the new estimation approach yields nearly unbiased estimates. An application to real data is also considered for illustrative purposes. • Circular data. • Circular von Mises regression. • Modified score functions. • Novel estimation approach for the von Mises regression. [ABSTRACT FROM AUTHOR]

Changes on temperature patterns, on a local scale, are perceived by individuals as the most direct indicators of global warming and climate change. As a specific example, for an Atlantic climate location, spring and fall seasons should present a mild transition between winter and summer, and summer and winter, respectively. By observing daily temperature curves along time, being each curve attached to a certain calendar day, a regression model for these variables (temperature curve as covariate and calendar day as response) would be useful for modeling their relation for a certain period. In addition, temperature changes could be assessed by prediction and observation comparisons in the long run. Such a model is presented and studied in this work, considering a nonparametric Nadaraya–Watson-type estimator for functional covariate and circular response. The asymptotic bias and variance of this estimator, as well as its asymptotic distribution are derived. Its finite sample performance is evaluated in a simulation study and the proposal is applied to investigate a real-data set concerning temperature curves. [ABSTRACT FROM AUTHOR]

A new data-based smoothing parameter for circular kernel density (and its derivatives) estimation is proposed. Following the plug-in ideas, unknown quantities on an optimal smoothing parameter are replaced by suitable estimates. This paper provides a circular version of the well-known Sheather and Jones bandwidths (J R Stat Soc Ser B Stat Methodol 53(3):683–690, 1991. ), with direct and solve-the-equation plug-in rules. Theoretical support for our developments, related to the asymptotic mean squared error of the estimator of the density, its derivatives, and its functionals, for circular data, are provided. The proposed selectors are compared with previous data-based smoothing parameters for circular kernel density estimation. This paper also contributes to the study of the optimal kernel for circular data. An illustration of the proposed plug-in rules is also shown using real data on the time of car accidents. [ABSTRACT FROM AUTHOR]

Many classical methods have been proposed to compute circular-circular correlation coefficients. However, these classical methods might be very sensitive to outliers in the data set. To date, no work has suggested a robust method to estimate a circular-circular correlation coefficient. The present paper aims to propose two robust methods to compute a circular-circular correlation coefficient when the circular data has outliers. The first method is computed based on the circular median, rMed, and the second on the circular trimmed mean, rTrim. A simulation study is conducted for two circular distributions: the wrapped normal and wrapped Cauchy distributions. The simulation and practical example show that the results of rMed are close to the results of classical methods. In contrast, the rTrim gives the best results and is the least affected by outliers, even with a high percentage of outliers. [ABSTRACT FROM AUTHOR]

Directional data appears in several branches of research. In some cases, those directional variables are only defined in subsets of the K-dimensional unit sphere. For example, in some applications, angles as measured responses are limited on the positive orthant. Analysis on subsets of the K-dimensional unit sphere is challenging and nowadays there are not many proposals that discuss this topic. Thus, from a methodological point of view, it is important to have probability distributions defined on bounded subsets of the K-dimensional unit sphere. Specifically, in this paper, we introduce a nonparametric Bayesian model to describe directional variables restricted to the first orthant. This model is based on a Dirichlet process mixture model with multivariate projected Gamma densities as kernel distributions. We show how to carry out inference for the proposed model based on a slice sampling scheme. The proposed methodology is illustrated using simulated data sets as well as a real data set. [ABSTRACT FROM AUTHOR]

Numerous testing procedures for directional data have been proposed over the years and a natural question that springs is which to use and when. The aim of this paper is to answer this question, via a large scale Monte Carlo simulation study that covers circular and spherical data for the two mean directions problem. The results evidently signify that tests assuming equal concentration parameters should be avoided as they tend to inflate the test size, while the heterogeneous test that does not make this assumption is to be preferred, but unfortunately only with large sample sizes. Permutation calibration does not improve the performance of any testing procedure, whereas bootstrap does. Specifically, bootstrap calibrated tests exhibited superior performance; they attain the type I error in the vast majority of the case scenarios examined and possess nearly indistinguishable empirical power levels. Finally, examples with real data illustrate the performance of the bootstrap calibrated tests. [ABSTRACT FROM AUTHOR]

Projected distributions have proved to be useful in the study of circular and directional data. Although any multivariate distribution can be used to produce a projected model, these distributions are typically parametric. In this article we consider a multivariate Pólya tree on R k and project it to the unit hypersphere S k to define a new Bayesian nonparametric model for directional data. We study the properties of the proposed model and in particular, concentrate on the implied conditional distributions of some directions given the others to define a directional–directional regression model. We also define a multivariate linear regression model with Pólya tree errors and project it to define a linear-directional regression model. We obtain the posterior characterisation of all models via their full conditional distributions. Metropolis-Hastings steps are required, where random walk proposal distributions are optimised with a novel adaptation scheme. We show the performance of our models with simulated and real datasets. [ABSTRACT FROM AUTHOR]

In directional statistics, the von Mises distribution is a key element in the analysis of circular data. While there is a general agreement regarding the estimation of its location parameter μ, several methods have been proposed to estimate the concentration parameter κ. We here provide a thorough evaluation of the behavior of 12 such estimators for datasets of size N ranging from 2 to 8192 generated with a κ ranging from 0 to 100. We provide detailed results as well as a global analysis of the results, showing that (1) for a given κ, most estimators have behaviors that are very similar for large datasets ( N ≥ 16 ) and more variable for small datasets, and (2) for a given estimator, results are very similar if we consider the mean absolute error for κ ≤ 1 and the mean relative absolute error for κ ≥ 1. [ABSTRACT FROM AUTHOR]

AbstractThis article presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of a conditional characteristic is carried out nonparametrically, by maximizing the circular local likelihood, and the estimator is shown to be asymptotically normal. The problem of selecting the smoothing parameter is also addressed, as well as bias and variance computation. The performance of the estimation method in practice is studied through an extensive simulation study, where we cover the cases of Gaussian, Bernoulli, Poisson, and Gamma distributed responses. The generality of our approach is illustrated with several real-data examples from different fields. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

The aim of this study is to propose two new cut-off points for outlier detection in univariate circular data using the concept of circular distance. The first cut-off point involves using a quantile of the gamma distribution based on adjusted circular distances, whereas the second cut-off point employs the upper fence of a modified boxplot for skewed data. Simulation studies are conducted using both uncontaminated and contaminated data, and the performance of the proposed cut-off points is evaluated in the proportion of outliers, probability of all outliers being successfully detected, probability of outliers being falsely detected as inliers (masking effect), and probability of inliers detected as outliers (swamping effect). Real data examples are also used to demonstrate the efficacy of the proposed cut-off points. The results of the simulation and real data experiments show that the proposed cut-off point involves using a quantile of the gamma distribution based on adjusted circular distances and is successful in outlier detection compared to the existing cut-off points. [ABSTRACT FROM AUTHOR]

A rose diagram is a representation that circularly organizes data with the bin width as the central angle. This diagram is widely used to display and summarize circular data. Some studies have proposed the selector of bin width based on data. However, only a few papers have discussed the property of these selectors from a statistical perspective. Thus, this study aims to provide a data-based bin width selector for rose diagrams using a statistical approach. We consider that the radius of the rose diagram is a nonparametric estimator of the square root of two times the circular density. We derive the mean integrated square error of the rose diagram and its optimal bin width and propose two new selectors: normal reference rule and biased cross-validation. We show that biased cross-validation converges to its optimizer. Additionally, we propose a polygon rose diagram to enhance the rose diagram. [ABSTRACT FROM AUTHOR]

Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal data), rendering spurious the use of PCA on it due to the periodicity of its support. This paper introduces Toroidal Ridge PCA (TR-PCA), a novel construction of PCA for bivariate circular data that leverages the concept of density ridges as a flexible first principal component analog. Two reference bivariate circular distributions, the bivariate sine von Mises and the bivariate wrapped Cauchy, are employed as the parametric distributional basis of TR-PCA. Efficient algorithms are presented to compute density ridges for these two distribution models. A complete PCA methodology adapted to toroidal data (including scores, variance decomposition, and resolution of edge cases) is introduced and implemented in the companion R package ridgetorus. The usefulness of TR-PCA is showcased with a novel case study involving the analysis of ocean currents on the coast of Santa Barbara. [ABSTRACT FROM AUTHOR]

The statistical techniques which are developed for the analysis of data in the linear number system cannot be applied to directional data directly. Circular data may be discontinuous in some principal interval. These discontinuities cause failure results in the circular statistics. Because of that the proposed wrapping operator must be used for data, which are defined in the discontinuous range. However, in both continuity and discontinuity, the wrapping operator works correctly. The most common preferred directions for circular data are circular mean and variance summarizing and comparing them. Although circular data has a very important role in statistics, the literature is weak in terms of statistical analysis of circular data. It creates a gap in this field. This study examines the preferred direction of circular data to fill this gap and presents a new measure of preferred direction for circular data using angular wrapping. Four different artificial and three real datasets are employed to evaluate the performance of the proposed methods. The results demonstrate the superiority of the proposed methods in terms of the absolute error and absolute percentage error. Consequently, it has been seen that the proposed methods give more consistent and more accurate results than the vectorial methods. [ABSTRACT FROM AUTHOR]

The score‐driven approach to time series modelling is able to handle circular data and switching regimes with intra‐regime dynamics. Furthermore it enables a dynamic model to be fitted to a linear and a circular variable when their joint distribution is a cylinder. The viability of the new method is illustrated by estimating models for hourly data on wind direction and speed in Galicia, north‐west Spain. The modelling of intra‐regime dynamics is shown to be of critical importance. [ABSTRACT FROM AUTHOR]

A nonparametric test labelled 'Rao Spacing-frequencies test' is explored and developed for testing whether two circular samples come from the same population. Its exact distribution and performance relative to comparable tests such as the Wheeler-Watson test and the Dixon test in small samples, are discussed. Although this test statistic is shown to be asymptotically normal, as one would expect, this large sample distribution does not provide satisfactory approximations for small to moderate samples. Exact critical values for small samples are obtained and tables provided here, using combinatorial techniques, and asymptotic critical regions are assessed against these. For moderate sample sizes in-between i.e. when the samples are too large making combinatorial techniques computationally prohibitive but yet asymptotic regions do not provide a good approximation, we provide a simple Monte Carlo procedure that gives very accurate critical values. As is well-known, the large number of usual rank-based tests are not applicable in the context of circular data since the values of such ranks depend on the arbitrary choice of origin and the sense of rotation used (clockwise or anti-clockwise). Tests that are invariant under the group of rotations, depend on the data through the so-called 'spacing frequencies', the frequencies of one sample that fall in between the spacings (or gaps) made by the other. The Wheeler-Watson, Dixon, and the proposed Rao tests are of this form and are explicitly useful for circular data, but they also have the added advantage of being valid and useful for comparing any two samples on the real line. Our study and simulations establish the 'Rao spacing-frequencies test' as a desirable, and indeed preferable test in a wide variety of contexts for comparing two circular samples, and as a viable competitor even for data on the real line. Computational help for implementing any of these tests, is made available online "TwoCircles" R package and is part of this paper.

Circular statistics have been developed and used in a wide range of branches of knowledge related to the study and observation of the Earth, such as physical, geographical, ecological, and biological sciences. Both to facilitate its use by a less specialised community and to extend its analysis within the research community, this work presents the application of circular statistics in QGIS, an open-source Geographic Information Systems, through the design and implementation of a novel and complete plugin, named QCircularStats. This free and open-source plugin provides a comprehensive, understandable, and visual way to conduct circular analysis over remote sensing data. The behaviour of the proposed QCircularStats is evaluated over real satellite data. Particularly, data on wind speed and direction over the oceans collected by the microwave sensor allocated on the QuikSCAT satellite have been considered. Results obtained demonstrate the performance, functionality, and versatility of the implemented plugin.

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. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of statistical hypotheses testing in circular data under weighted sampling. The most powerful test has been obtained when the sampling is subjected to a weight function. Different weight functions are examined for the von Misses distribution. For the same weight function, the critical values and the power of the test can be calculated analytically, and for some, we need to use a numerical method. The simulation study shows that the power of the test increased as the weighted circular distribution is considered in replace of the original circular distribution and the sample data increased. A real-data example has been carried out to show the performance of our method. [ABSTRACT FROM AUTHOR]

We propose a class of goodness-of-fit test procedures for arbitrary parametric families of circular distributions with unknown parameters. The tests make use of the specific form of the characteristic function of the family being tested, and are shown to be consistent. We derive the asymptotic null distribution and suggest that the new method be implemented using a bootstrap resampling technique that approximates this distribution consistently. As an illustration, we then specialize this method to testing whether a given data set is from the von Mises distribution, a model that is commonly used and for which considerable theory has been developed. An extensive Monte Carlo study is carried out to compare the new tests with other existing omnibus tests for this model. An application involving five real data sets is provided in order to illustrate the new procedure.

Copyright of Journal of Economics & Administrative Sciences is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Circular data can be found across many areas of science, for instance meteorology (e.g., wind directions), ecology (e.g., animal movement directions), or medicine (e.g., seasonality in disease onset). The special nature of these data means that conventional methods for non-periodic data are no longer valid. In this paper, we consider wrapped Gaussian processes and introduce a spatial model for circular data that allow for non-stationarity in the mean and the covariance structure of Gaussian random fields. We use the empirical equivalence between Gaussian random fields and Gaussian Markov random fields which allows us to considerably reduce computational complexity by exploiting the sparseness of the precision matrix of the associated Gaussian Markov random field. Furthermore, we develop tunable priors, inspired by the penalized complexity prior framework, that shrink the model toward a less flexible base model with stationary mean and covariance function. Posterior estimation is done via Markov chain Monte Carlo simulation. The performance of the model is evaluated in a simulation study. Finally, the model is applied to analyzing wind directions in Germany. [ABSTRACT FROM AUTHOR]

Clustering algorithms can be used to create an outlier detection procedure in univariate circular data. The circular distance between each point of angular observation in circular data is used to calculate the similarity measure to appropriately group observations. In this paper, we present a clustering-based procedure for detecting outliers in univariate circular biological data using various similarity distance measures. Three circular similarity distance measures; Satari distance, Di distance and Chang-chien distance were used to detect outliers using a single-linkage clustering algorithm. Satari distance and Di distance are two similarity measures that have similar formulas for univariate circular data. This study aims to develop and demonstrate the effectiveness of the proposed clusteringbased procedure with various similarity distance measures in detecting outliers. The circular similarity distance of SL-Satari/Di and other similarity measures, including SL-Chang, were compared at various dendrogram cutting points. It is found that a clustering-based procedure using a single-linkage algorithm with various similarity distances is a practical and promising approach to detect outliers in univariate circular data, particularly for biological data. According to the results, the SL-Satari/Di distance outperformed the SL-Chang distance for certain data conditions. [ABSTRACT FROM AUTHOR]

Adimensionality reduction method for high-dimensional circular data is developed, which is based on a principal component analysis (PCA) of data points on a torus. Adopting a geometrical view of PCA, various distance measures on a torus are introduced and the associated problem of projecting data onto the principal subspaces is discussed. The main idea is that the (periodicity-induced) projection error can be minimized by transforming the data such that the maximal gap of the sampling is shifted to the periodic boundary. In a second step, the covariance matrix and its eigendecomposition can be computed in a standard manner. Adopting molecular dynamics simulations of two well-established biomolecular systems (Aib9 and villin headpiece), the potential of the method to analyze the dynamics of backbone dihedral angles is demonstrated. The new approach allows for a robust and well-defined construction of metastable states and provides low-dimensional reaction coordinates that accurately describe the free energy landscape. Moreover, it offers a direct interpretation of covariances and principal components in terms of the angular variables. Apart from its application to PCA, the method of maximal gap shifting is general and can be applied to any other dimensionality reduction method for circular data. [ABSTRACT FROM AUTHOR]

The Cardioid (C) distribution is one of the most important models for modeling circular data. Although some of its structural properties have been derived, this distribution is not appropriate for asymmetry and multimodal phenomena in the circle, and then extensions are required. There are various general methods that can be used to produce circular distributions. This paper proposes four extensions of the C distribution based on the beta, Kumaraswamy, gamma, and Marshall–Olkin generators. We obtain a unique linear representation of their densities and some mathematical properties. Inference procedures for the parameters are also investigated. We perform two applications on real data, where the new models are compared to the C distribution and one of its extensions.

In the intelligent weather forecast business, the detection of shear line systems in 2-D numerical wind fields is a critical research topic for analysis and predict severe convective weather intelligently. However, the actual wind field is quite complicated, which contains more than ten types of wind field patterns and random noise, which brings challenges to the identification of the shear line. In this paper, a kurtosis based descriptive statistic of circular data was proposed to detect shear pattern from other types of flow patterns. In the experimental part, the classification characteristics of descriptive statistics were analyzed qualitatively and quantitatively in ten types of simulated flow patterns, which verified the identify advantage of kurtosis on the shear field. Finally, a shear line detection algorithm based on kurtosis is designed to applying to the actual wind field, and it has the advantage of global detection, better robustness, and faster execution. [ABSTRACT FROM AUTHOR]

Testing procedures for assessing a parametric regression model with a circular response and an R d -valued covariate are proposed and analysed in this work. The test statistics are based on a circular distance comparing a (non-smoothed or smoothed) parametric circular regression estimator and a nonparametric one. Two bootstrap procedures for calibrating the tests in practice are also presented. Finite sample performance of the tests in different scenarios is analysed by simulations and illustrated with real data examples. [ABSTRACT FROM AUTHOR]

In this paper, we derive asymptotic expressions for the mean integrated squared error of a class of delta sequence density estimators for circular data. This class includes the class of kernel density estimators usually considered in the literature, as well as a new class that is closer in spirit to the class of Parzen–Rosenblatt estimators for linear data. For these two classes of kernel density estimators, a Fourier series-based direct plug-in approach for bandwidth selection is presented. The proposed bandwidth selector has a n − 1 / 2 relative convergence rate whenever the underlying density is smooth enough and the simulation results testify that it presents a very good finite sample performance against other bandwidth selectors in the literature. [ABSTRACT FROM AUTHOR]

Regular changes in the environment and biological responses generate seasonal patterns in the reproduction in small ruminants. Breeding seasonality is a significant constraint impacting efficiency of lamb production. However, seasonality‐related traits present a special peculiarity from a statistical point of view being circular data (day of year running 1:365). Recently, circular mixed models have been developed on the basis of the von Mises distribution and were applied to analyse lambing day distribution recorded from five major Canadian sheep breeds (Rideau Arcott, Romanov, Dorset, Suffolk and Polypay). In a simulation study, the linear model was not able to capture the variance components simulated under the circular paradigm; however, the von Mises model evidenced its ability to infer the variance components of simulated circular records. Using real data of sheep, mostly negligible variances were observed for additive genetic effect when using a linear model on circular data values. In contrast, when using the von Mises model, genetic variances were different across breeds, and it raises the possibility to delay the peak of reproduction and to change the seasonality of the ewes. However, a large variance was captured by flock‐year effects emphasizing the strong influence of management in lambing seasons for Canadian sheep populations. Finally, the results suggest the potential of using the von Mises model to analyse circular data, and further research is needed for better understand the complexity of this trait and the von Mises models. [ABSTRACT FROM AUTHOR]

The statistical tests under classical statistics can be only applied when the data is linear and has certain observations. The existing statistical tests cannot be applied for circular/angles data. In this paper, the Watson-Williams test under neutrosophic is introduced to analyze having uncertain, imprecise, and indeterminate circular/angles data. The neutrosophic test statistic is introduced and applied to wind direction data. From the real example and simulation study, it can be concluded the proposed neutrosophic Watson-Williams test performs better than the Watson-Williams test under classical statistics.

In this paper, we apply the multiplicative bias correction (MBC) techniques for von Mises (vM) kernel density estimator in the context of circular data. Some properties of the MBC-vM kernel circular density estimators (bias, variance and mean integrated squared error) are shown. The choice of bandwidth is investigated by adapting the popular cross-validation techniques. The performances of the MBC estimators based on vM kernel are illustrated by a simulation study and real application for circular data. In general, in terms of integrated squared bias (ISB) and integrated squared error (ISE), the proposed estimators outperform the standard vM kernel estimator. [ABSTRACT FROM AUTHOR]

The general projected normal distribution is a flexible distribution family that is widely used for modelling circular data. It is constructed by projecting the bivariate normal distribution onto the unit circle. Maximum likelihood estimation for the general projected normal distribution was considered for the special cases of Σ = I as well as Σ = σ 2 I . In this study, we consider the problem of maximum likelihood estimation assuming general form of Σ. EM-algorithm and Newton Raphson method are formulated and used to obtain approximations for the final estimators. A simulation study is conducted to evaluate the performance of the estimated parameters. In general, the obtained estimators show consistent behaviour where EM-algorithm has better performance compared to the Newton Raphson method. Moreover, extension for the regression problem is introduced where EM-algorithm is developed. Two examples are provided to demonstrate the proposed estimators in real applications. [ABSTRACT FROM AUTHOR]

In earlier studies of circular data, the corresponding probability distributions considered were mostly assumed to be symmetric. However, the assumption of symmetry may not be meaningful for some data. Thus there has been increased interest, more recently, in developing skewed circular distributions. In this article we introduce three skewed circular models based on inverse stereographic projection (ISP), originally introduced by Minh and Farnum (Comput. Stat.–Theory Methods, 32, 1–9, 2003), by considering three different versions of skewed-t distribution on real line considered in the literature, namely skewed-t by Azzalini (Scand. J. Stat., 12, 171–178, 1985), two-piece skewed-t, (seemingly first considered in Gibbons and Mylroie Appl. Phys. Lett., 22, 568–569, 1973 and later by Fernández and Steel J. Amer. Statist. Assoc., 93, 359–371 1998) and skewed-t by Jones and Faddy (J. R. Stat. Soc. Ser. B (Stat. Methodol.), 65, 159–174, 2003). Unimodality and skewness of the resulting distributions are addressed in this paper. Further, real data sets are used to illustrate the application of the new models. It is found that under certain condition on the original scaling parameter, the resulting distributions may be unimodal. Furthermore, the study in this paper concludes that ISP circular distributions obtained from skewed distributions on the real line may provide an attractive alternative to other asymmetric unimodal circular distributions, especially when combined with a mixture of uniform circular distribution. [ABSTRACT FROM AUTHOR]

One way of defining probability distributions for circular variables (directions in two dimensions) is to radially project probability distributions, originally defined on R 2 , to the unit circle. Projected distributions have proved to be useful in the study of circular and directional data. Although any bivariate distribution can be used to produce a projected circular model, these distributions are typically parametric. In this article, we consider a bivariate Pólya tree on R 2 and project it to the unit circle to define a new Bayesian nonparametric model for circular data. We study the properties of the proposed model, obtain its posterior characterization and show its performance with simulated and real datasets. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]

Dates have great importance in cancer diseases. However, the date variables themselves are not analyzed. This study aims to evaluate the descriptive statistics of diagnosis, operation, and last examination dates in gastric carcinoma patients by circular analysis methods. Totally 502 gastric carcinoma patients were enrolled in the study. The mean month of diagnosis date was found in nearly November (∼10.86) for females and May (∼5.17) for male patients. The mean month of operation date was found March (∼3.24) for females, and July & August (∼7.79) for males. The mean month of the last examination date was found as February & March (∼2.61) for females, and May (∼4.85) for males. Moreover, the mean day of the week for diagnosis date was found Thursday (∼5.50) for both female and male patients. The fitting of distributions of all variables was checked, also, according to von Mises, Rayleigh, and Kuiper's tests. When the days and months were analyzed by classical descriptive statistics, the results were obtained completely different from the circular analyses results. Therefore, the dates and times should be analyzed in certain diseases to give an idea for physicians. [ABSTRACT FROM AUTHOR]

The aim of this study is to analyze suicide cases with circular data analysis and to compare them with the standard linear analysis method and to guide the implementation of long-term social protective programs. Circular data analysis was used as method. However, standard linear statistics method was also used to compare the results of circular data analysis. Men constitute 74.91% of 15731 cases included in the study. Disease (39.84%) has been identified as the highest risk factor. Despite having a low concentration, the most suicide occurred in May (9.43%). Furthermore, a significant relationship was found between suicide causes and gender and suicide causes and months (p<0.05). In the analyses performed by circular data analysis, although the mean direction of suicides indicated May 29 (148.11°), suicides spread throughout the year according to circular variance (0.96). It was determined that the mean directions of suicide causes among from 1 April (90.02°) to 19 July (199.69°), so the concentration of suicide was in this interval. However, according to the distribution measures, all causes of suicide, except educational failure, showed a multimodal distribution. It can be stated that at least one sample distribution, mean direction, condensation parameter differs from other sample parameters in terms of itself species (p<0.05). Suicide cases were seen more common among men and during the spring -summer months. It is recommended to take preventive measures according to risk factors in ord er to prevent suicides, especially in periods determined. [ABSTRACT FROM AUTHOR]

Analysis of some real phenomena involve directional variables that by their nature are defined only in certain subsets of the k-dimensional unit sphere, S k. For example, when working with axial data, the support of the associated directional variables turns out to be the interval (0 , π ]. Thus, from a methodological point of view it is important to have probability distributions defined in bounded subsets of S k. Specifically, in order to describe directional variables restricted to the first orthant, in this paper we introduce the Multivariate Projected Gamma model (MPG). This model is flexible enough and treats observations as projections onto the unit sphere of unobserved responses from a multivariate distribution which is generated as a product of k independent univariate Gamma distributions. Inference about the parameters of the model is based on samples from the corresponding joint posterior density, which is obtained using a Gibbs sampling after the introduction of suitable latent variables. The proposed methodology is illustrated using simulated data sets as well as a real data set. [ABSTRACT FROM AUTHOR]