Mean-Based Breakpoint Selection on Circular Histogram

Circular histogram represents the statistical distribution of circular data; the H component histogram of HSI color model is a typical example of the circular histogram. When using H component to segment color image, a feasible way is to transform the circular histogram into a linear histogram, and then, the mature gray image thresholding methods are used on the linear histogram to select the threshold value. Thus, the reasonable selection of the breakpoint on circular histogram to linearize the circular histogram is the key. In this paper, based on the angles mean on circular histogram and the line mean on linear histogram, a simple breakpoint selection criterion is proposed, and the suitable range of this method is analyzed. Compared with the existing breakpoint selection criteria based on Lorenz curve and cumulative distribution entropy, the proposed method has the advantages of simple expression and less calculation and does not depend on the direction of rotation.

Score-Driven Time Series Models

The construction of score-driven filters for nonlinear time series models is described, and they are shown to apply over a wide range of disciplines. Their theoretical and practical advantages over other methods are highlighted. Topics covered include robust time series modeling, conditional heteroscedasticity, count data, dynamic correlation and association, censoring, circular data, and switching regimes. Expected final online publication date for the Annual Review of Statistics and Its Application, Volume 9 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Advice on comparing two independent samples of circular data in biology

Many biological variables are recorded on a circular scale and therefore need different statistical treatment. A common question that is asked of such circular data involves comparison between two groups: Are the populations from which the two samples are drawn differently distributed around the circle? We compared 18 tests for such situations (by simulation) in terms of both abilities to control Type-I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of Type-I error in all our simulated situations. Of these eight, we were able to identify the Watson’s U2 test and a MANOVA approach, based on trigonometric functions of the data, as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watson’s U2 test or MANOVA approach when comparing two samples of circular data.

Radar Circular Data Analysis Using a New Watson’s Goodness of Test under Complexity

Watson’s test is applied to test either the given angular data follows the specified distribution or not. The existing Watson’s test under classical statistics is applied when there is no uncertainty and indeterminacy in sample size or angular data. Under indeterminacy, the existing Watson’s test cannot be applied for testing purposes. Neutrosophic statistics is an alternative to classical statistics for this kind of situation. The Watson’s test under neutrosophic statistics is proposed in this paper. The test statistic of Watson’s test is introduced first. The operational procedure of the proposed Watson’s test is discussed with the help of radar data. From the data analysis and simulation study, it is concluded the proposed Watson’s test is efficient than the existing Watson’s test.

The multivariate analysis of variance as a powerful approach for circular data

A broad range of scientific studies involve taking measurements on a circular rather than linear scale (often times or orientations). For linear measures there is a well-established statistical toolkit based on linear modelling to explore the associations between this focal variable and potentially several explanatory factors and covariates. However, most statistical testing of circular statistics is much simpler: often involving either testing whether variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two levels is supported. Here we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as effective as the most-commonly used tests in these simple situations, while additionally it offers extension to multi-factorial modelling that these conventional tests do not. This, in combination with recent developments in Bayesian approaches, offers a substantial broadening of the scientific questions that can be addressed statistically with circular data.

Generalized Cardioid Distributions for Circular Data Analysis

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.

Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection

In this work, we deal with a robust fitting of a wrapped normal model to multivariate circular data. Robust estimation is supposed to mitigate the adverse effects of outliers on inference. Furthermore, the use of a proper robust method leads to the definition of effective outlier detection rules. Robust fitting is achieved by a suitable modification of a classification-expectation-maximization algorithm that has been developed to perform a maximum likelihood estimation of the parameters of a multivariate wrapped normal distribution. The modification concerns the use of complete-data estimating equations that involve a set of data dependent weights aimed to downweight the effect of possible outliers. Several robust techniques are considered to define weights. The finite sample behavior of the resulting proposed methods is investigated by some numerical studies and real data examples.