Mises Distribution Research Articles

Sexual and ontogenetic morphometric variation in Xiphopenaeus kroyeri (Crustacea, Decapoda, Penaeidae): a new approach with linear and angular morphometric data

The present study evaluates the ontogenetic/sexual morphometric variation in Xiphopenaeus kroyeri. Sampling was from July 2001 to June 2003 at Ubatuba, São Paulo, Brazil. Animals were sexed and measured (cephalothorax length-CC, partial of the rostral spine-CPR, rostral spine-CR and rostral spine angulation-AR). Data analysis included linear morphometric analysis: equation ln y = ln a + ln b (sex/ontogeny fitting), k-means method (ontogenetic classification), analysis of covariance (morphological maturity), removal of the allometric effect, verification of parametricity and collinearity, principal component (PCA) and linear discriminant analysis (visualization of tendencies), permutational multivariate analysis of variance (hypothesis test). In addition, circular analysis was undertaken: circular normal distribution and concentration parameter, circular analysis of variance (hypothesis test), PCA (observe tendencies) and linear-circular regression (ontogenetic trajectory, RA-dependent variable, CL-independent variable). Morphological changes in the cephalothorax, in the adult stage, may be related to the increase in size of the gonads during sexual maturation and to the development of gills during the transition from arthrobranch (juvenile) to dendrobranch (adult). The rostral spine, in the adult stage, tends to become more elongated and more sharply angled. This feature may be related to predation pressure on larger specimens (adults), knowing that throughout its ontogeny the rostral spine of this species assumes phenotypic traits that make swallowing more difficult for predators.

The Seasonality of Acute Attack of Primary Angle-Closure Glaucoma in Beijing, China

In this study, the seasonality of acute attack of primary angle-closure glaucoma (PACG) was analysed. This retrospective case series included 283 patients (200 women, 83 men; mean age, 68.2 ± 10.3 years; range, 37–96 years) with acute attack of PACG from a university-based clinic over 4 years. Patients’ age and sex, and the date and season of onset of PACG attack, were analysed. Descriptive analysis and von Mises distribution were used for statistical analysis. The highest incidence of acute attack of PACG was observed in those aged 60–69 years (34.6%). Descriptive analysis showed that the incidence was greater in June and July for men, November for women, and November for the entire sample. An angular plot (using von Mises distribution) of the individual dates of onset revealed the estimated peak onset on September 11, November 8, and October 28 for men, women, and both, respectively. Integration of the results from the two analyses revealed the incidence to be higher in the summer and winter for men, and in the winter for women and for the entire sample. More females than males were affected. Monthly and seasonal variations in onset were observed, which might be related to weather changes.

Transformation of circular random variables based on circular distribution functions

In this paper, we propose a new transformation of circular random variables based on circular distribution functions, which we shall call inverse distribution function (id f ) transformation. We show that M?bius transformation is a special case of our id f transformation. Very general results are provided for the properties of the proposed family of id f transformations, including their trigonometric moments, maximum entropy, random variate generation, finite mixture and modality properties. In particular, we shall focus our attention on a subfamily of the general family when id f transformation is based on the cardioid circular distribution function. Modality and shape properties are investigated for this subfamily. In addition, we obtain further statistical properties for the resulting distribution by applying the id f transformation to a random variable following a von Mises distribution. In fact, we shall introduce the Cardioid-von Mises (CvM) distribution and estimate its parameters by the maximum likelihood method. Finally, an application of CvM family and its inferential methods are illustrated using a real data set containing times of gun crimes in Pittsburgh, Pennsylvania.

Analysis of Peak and Statistical Spectrum of Random Nonreturn-to-Zero Digital Signals

It is important to understand the spectral profile of the noise sources in electromagnetic compatibility (EMC) design. One of the various noise sources in modern electronics is the nonreturn-to-zero (NRZ) signal, a common digital signal format. Although conventionally the power spectral density of NRZ signal can be calculated based on Wiener–Khinchin theorem, which gives the average power per unit bandwidth, some specific properties are still unstudied. This paper analyzes 1) the maximum (peak) level, and 2) the probability density function (PDF) of the spectrum of NRZ signals. The importance of the peak level is that it represents the worst-case interference that may be produced by an NRZ trace, while the PDF is a more complete description of the spectral characteristics. The peak power is obtained through an algorithm and then well fitted, for most frequencies, by a formula, whereas the PDFs are represented in closed-form by using the central limit theorem. Based on the analysis, the peak level is found to have the same sinc shape but roughly 30-dB larger than the average power, in a 1-MHz bandwidth channel. The PDF is found to have the circular normal distribution at most frequencies, but is degenerated at frequencies of integer multiples of half-bit-rate. Measurement and simulation results verify the correctness of the proposed theory.

Bayesian estimation and hypothesis tests for a circular Generalized Linear Model

Motivated by a study from cognitive psychology, we develop a Generalized Linear Model for circular data within the Bayesian framework, using the von Mises distribution. Although circular data arise in a wide variety of scientific fields, the number of methods for their analysis is limited. Our model allows inclusion of both continuous and categorical covariates. In a frequentist setting, this type of model is plagued by the likelihood surface of its regression coefficients, which is not logarithmically concave. In a Bayesian context, a weakly informative prior solves this issue, while for other parametersnoninformative priors are available. In addition to an MCMC sampling algorithm, we develop Bayesian hypothesis tests based on the Bayes factor for both equality and inequality constrained hypotheses. In a simulation study, it can be seen that our method performs well. The analyses are available in the package CircGLMBayes. Finally, we apply this model to a dataset from experimental psychology, and show that it provides valuable insight for applied researchers. Extensions to dependent observations are within reach by means of the multivariate von Mises distribution.

Objective assessment of perceived effort in listening by employing EEG feature.

The adjustment of hearing aid devices can heavily depend on the subjective feedback of the patients. Our aim is to investigate measures that can be used objectively to state a subject's listening effort. To obtain a comprehensive and reliable measure as an indicator for a person's listening effort, we need to have a better understanding of electroencephalograpic (EEG) activities. Decoding EEG signals specifically by the analysis of the instantaneous phase information has been a new trend in the last decades. Throughout many studies conducted in the past, it has been shown that the instantaneous phase of oscillatory signals reset in relation to various cognitive processes. This is based on a hypothesis presented for the generation of event related potentials. In this study, we measure the degree of phase re-organization through fitting a von Mises distribution to EEG recordings. The concentration parameter of a von Mises distribution has been shown as an informative feature for reflecting the level of attention. This feature has been used for predicting the listening effort and the results are compared among three different hearing aid settings.

Location wise comparison of mixture distributions for assessment of wind power potential: A parametric study

ABSTRACTScientific literature discussed various types of mixture models and models derived from maximum entropy principle using short-term wind speed data for their relative assessment. The literature on suitability of these mixture models for long-term data is rarely available. However, for correct assessment of wind power potential both wind speed and wind direction are equally important. Therefore, in this paper, both wind speed and wind direction are simultaneously analyzed using several types of mixture distribution and compared the same with conventional Weibull distribution. For wind speed and wind power density assessment, the mixture distributions such as Weibull--Weibull distribution, Gamma--Weibull distribution, Truncated Normal--Weibull distribution, Truncated Normal--Normal distribution, proposed Truncated Normal--Gamma distribution and Gamma--Gamma distribution along with MEP-distribution are compared with conventional 2-parameter Weibull distribution. Similarly, for wind direction analysis, the finite mixtures of von-Mises distribution are compared with conventional von-Mises distribution. Judgment criteria include R2, RMSE, Kolmogorov--Smirnov test and relative percentage error in wind power density. The sites selected are the three onshore locations of India, viz., Calcutta, Trivandrum, and Ahmedabad. The results show that for wind speed assessment, mixture distribution performs better than the conventional Weibull distribution for analyzing wind power density. However, location wise comparison of all mixture distribution is of prime importance. For wind direction analysis, finite mixture of two von-Mises distributions proved to be a suitable candidate for Indian climatology.

Quantifying rock fall probabilities and their temporal distribution associated with weather seasonality

Quantifying rock fall hazards requires information about their frequency and volumes. Previous studies have focused on quantifying rock fall volume–frequency relationships or the weather conditions antecedent to rock fall occurrences, and their potential use as prediction tools. This paper is focused on quantifying rock fall occurrence probabilities and presents approaches for quantifying rock fall temporal distributions. In particular, von Mises distributions allow direct correlation between seasonal weather variations and rock fall occurrences. The approaches are illustrated using a rock fall database along a railway corridor in the Canadian Cordillera, in which rock fall occurrences were correlated to the morphology and lithology. A Binomial probability distribution applied to the annual rock fall frequency suggests an average daily rock fall probability of 1 × 10−2 across the study area. However, circular (von Mises) distributions associated with weather trends in the area, and fitted to monthly rock fall records, allow estimation of daily rock fall probabilities in different months. This approach allows a direct correlation between rock fall frequencies and seasonal variations in weather conditions. The results suggest daily rock fall probabilities between 4 × 10−3 and 8 × 10−3 for April through July and up to 2.1 × 10−2 in October. Moreover, local peaks in rock fall monthly records are quantitatively explained through the seasonality of weather conditions. Similar values are obtained when applying the Binomial distribution to monthly records. However, this last approach does not show strong distribution fits and does not allow a correlation between rock fall frequencies and seasonal weather variations.

Influence of microbond test parameters on interfacial shear strength of fiber reinforced polymer-matrix composites

The microbond test commonly used to determine the interfacial shear strength (IFSS) of fiber-reinforced composites involves a number of experiment parameters that are not standardized in practice. This investigation is aimed to quantify and explain the influences of these parameters on the test results. We first validated the force-displacement curves and IFSS results of finite element simulated model pullout tests with that from experiments conducted at equivalent conditions. The von Mises and contact friction stress distributions from the simulation models were used to explain the influences of experimental parameters on IFSS from microbond test. The study shows that fiber diameter has the largest effect on IFSS. Bead size and blade position also have significant influences on the IFSS results from microbond tests. These testing parameters should be kept as close to constants as possible when conducting comparative microbond tests.

Hierarchical Bayesian measurement models for continuous reproduction of visual features from working memory.

The article presents Bayesian hierarchical modeling frameworks for two measurement models for visual working memory. The models can be applied to the distributions of responses on a circular feature dimension, as obtained with the continuous reproduction (a.k.a. delayed estimation) task. The first measurement model is a mixture model that describes the response distributions as a mixture of one (Zhang & Luck, 2008) or several (Bays, Catalao, & Husain, 2009) von-Mises distribution(s) and a uniform distribution. The second model is a novel, interference-based measurement model. We present parameter recovery simulations for both models, demonstrating that the hierarchical framework enables precise parameter estimates when a small number of trials are compensated by a large number of subjects. Simulations with the mixture model show that the Bayesian hierarchical framework minimizes the previously observed estimation bias for memory precision in conditions of low performance. Unbiased and reasonably precise parameter estimates can also be obtained from the interference measurement model, though some parameters of this model demand a relatively large amount of data for precise measurement. Both models are applied to two experimental data sets. Experiment 1 measures the effect of memory set size on the model parameters. Experiment 2 provides evidence for the assumption in the interference model that the target feature tends to be confused with features of those nontargets that are close to the target on the dimension used as retrieval cue.

Critical assessment of von Mises distribution and an infinite series ansatz for self-propelled particles

We consider a Vicsek model of self-propelled particles with bounded confidence, where each particle interacts only with neighbors that have a similar direction. Depending on parameters, the system exhibits a continuous or discontinuous polar phase transition from the isotropic phase to a phase with a preferred direction. In a recent paper (Lam, Schindler and Dauchot 2015 J. Stat. Mech. P10017) the von Mises distribution was proposed as an ansatz for polar ordering. In the present system the time evolution of the angular distribution can be solved in Fourier space. We compare the results of the Fourier analysis with the ones obtained by using the von Mises distribution ansatz. In the latter case the qualitative behavior of the system is recovered correctly. However, quantitatively there are serious deviations. We introduce an extended von Mises distribution ansatz such that a second term takes care of the next two Fourier modes. With the extended ansatz we find much better quantitative agreement. As an alternative approach we also use a Gaussian and a geometric series ansatz in Fourier space. The geometric series ansatz is analytically handable but fails for very weak noise, the Gaussian ansatz yields better results but it is not analytically treatable.

The Multivariate Generalised von Mises Distribution: Inference and Applications

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by extending some standard probabilistic modelling tools to the circular domain. First we introduce a new multivariate distribution over circular variables, called the multivariate Generalised von Mises (mGvM) distribution. This distribution can be constructed by restricting and renormalising a general multivariate Gaussian distribution to the unit hyper-torus. Previously proposed multivariate circular distributions are shown to be special cases of this construction. Second, we introduce a new probabilistic model for circular regression inspired by Gaussian Processes, and a method for probabilistic Principal Component Analysis with circular hidden variables. These models can leverage standard modelling tools (e.g. kernel functions and automatic relevance determination). Third, we show that the posterior distribution in these models is a mGvM distribution which enables development of an efficient variational free-energy scheme for performing approximate inference and approximate maximum-likelihood learning.

Analysis and probabilistic modeling of wind characteristics of an arch bridge using structural health monitoring data during typhoons

The accurate evaluation of wind characteristics and wind-induced structural responses during a typhoon is of significant importance for bridge design and safety assessment. This paper presents an expectation maximization (EM) algorithm-based angular-linear approach for probabilistic modeling of field-measured wind characteristics. The proposed method has been applied to model the wind speed and direction data during typhoons recorded by the structural health monitoring (SHM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. In the summer of 2015, three typhoons, i.e., Typhoon Chan-hom, Typhoon Soudelor and Typhoon Goni, made landfall in the east of China and then struck the Jiubao Bridge. By analyzing the wind monitoring data such as the wind speed and direction measured by three anemometers during typhoons, the wind characteristics during typhoons are derived, including the average wind speed and direction, turbulence intensity, gust factor, turbulence integral scale, and power spectral density (PSD). An EM algorithm-based angularlinear modeling approach is proposed for modeling the joint distribution of the wind speed and direction. For the marginal distribution of the wind speed, the finite mixture of two-parameter Weibull distribution is employed, and the finite mixture of von Mises distribution is used to represent the wind direction. The parameters of each distribution model are estimated by use of the EM algorithm, and the optimal model is determined by the values of R2 statistic and the Akaike

Development of Environmental Contours for Circular and Linear Metocean Variables

Probabilistic structural analysis of offshore structures is a demanding task due to high number of environmental variables and their uncertainties. Thus methods that reduce the computational effort are always welcomed and the environmental contours method is one of these favorite methods. But almost all the developed environmental contours method are limited to combination of linear metocean variables. Because of importance of design wave and wind direction especially in coastal and nearshore areas, this research is concentrated on development of environmental contours for combinations of circular and linear variables. These contours are derived from the Nataf transformation based approach and conditional modelling approach (CMA). In this paper the CMA was modified to be suitable for circular-linear variables. The circular variable is assumed to be the independent one and a mixture of von-Mises distributions was fitted to it. Linear variables were distributed conditionally on the circular variable. The regression between the distribution parameters and circular variable was set by Fourier series. Then, the Nataf- based model was applied to compare the results. The comparison shows that environmental contours based on the CMA illustrate the wave directionality effect much better than the Nataf-based model.

SB-robust estimation of mean direction for some new circular distributions

The most often used distribution for modelling directional data has been the circular normal (CN) (a.k.a. von-Mises) distribution. Recently Kato and Jones (K–J) introduced a family of distribution which includes the CN distribution as a special case. We study the SB-robustness of the circular mean functional (CMF) and show that the CMF is not SB-robust at the family of all symmetric Kato–Jones distributions but is SB-robust at sub-families with bounded parameters. It is also found to be SB-robust for certain sub-families of wrapped-t (WT) distributions, mixtures of K–J distributions and mixtures of K–J and WT distributions. The SB-robustness of the circular trimmed mean functional (CTMF) is also studied and it is found that the CTMF is SB-robust for larger sub-families of symmetric Kato–Jones distributions compared to that of CMF. The SB-robustness of the CMF for asymmetric families of distributions is studied and it is shown that CMF is SB-robust at a sub-family of asymmetric Kato–Jones distributions. The performance of CTM is compared with that of circular mean (CM) through extensive simulation. It is seen that CTM has better robustness properties than the CM both theoretically and practically. Some guidelines for choice of trimming proportion for CTM is given.

Recovery of orientation distribution function of MA2-1hp magnesium alloy exposed to equal-channel angular pressing

The problem of the recovery of the orientation distribution function (ODF) of a magnesium sample according to the approximation by circular normal distributions is considered. Initial data represent incomplete unnormalized X-ray pole figures (PFs). The choice of the procedure is related to its possible application for materials with the low symmetry of the sample, unique solution in the chosen class of functions, and measurement error stability of pole figures.

Moments of von Mises and Fisher distributions and applications.

The von Mises and Fisher distributions are spherical analogues to the Normal distribution on the unit circle and unit sphere, respectively. The computation of their moments, and in particular the second moment, usually involves solving tedious trigonometric integrals. Here we present a new method to compute the moments of spherical distributions, based on the divergence theorem. This method allows a clear derivation of the second moments and can be easily generalized to higher dimensions. In particular we note that, to our knowledge, the variance-covariance matrix of the three dimensional Fisher distribution has not previously been explicitly computed. While the emphasis of this paper lies in calculating the moments of spherical distributions, their usefulness is motivated by their relationship to population statistics in animal/cell movement models and demonstrated in applications to the modelling of sea turtle navigation, wolf movement and brain tumour growth.

Aeolian dune sediment flux variability over an annual cycle of wind

AbstractAeolian dune motion is thought to be driven by an annual cycle of sediment‐transporting wind events. Each wind event drives uneven motion of dune crestlines, yet dune crestlines align as a trend to an annual cycle of wind. Understanding the variability in dune motion over such a cycle aids the interpretation of aeolian cross‐stratification, often available only in the limiting exposure of core and outcrop. Digital elevation models obtained by light detection and ranging are used to estimate dune brink motion and sediment flux along the sinuous crestlines of crescentic dunes at White Sands gypsum dune field (south‐central New Mexico, USA) over an annual cycle of wind. In tandem, meteorological observations over the same annual cycle are used to drive a kinematic model of dune crestline motion. Wind‐driven kinematic modelling does well to predict the mean and overall variation in sediment flux with compass direction. Digital elevation model‐based estimations of brink motion and sediment flux reveal that dune motion and sediment flux very nearly follow a circular normal distribution. Dunes at White Sands were found to achieve steady mean values of lee surface dip direction, brink motion and sediment flux within a sample window the size of approximately six dunes of average crestline length. Due to the symmetrical distribution of dune motion about the average lee surface dip direction, uneven motion of dune crestlines averages to become motion of dune crestlines normal to a trend, as predicted by wind‐driven kinematic models.

Empirical Models of the Azimuthal Reception Angle—Part II: Adaptation of the Empirical Models in Analytical and Simulation Studies

This paper focuses on modeling of the statistical reception angle properties that are the result of the environmental influence on transmitted signals. Numerous measurements have shown that the statistical properties of angle of arrival (AOA) significantly depend on the type of propagation environment. In practice, this means that in the analytical and simulation studies, the use of statistical models of AOA required their adaptation to propagation conditions in research scenario. Despite the large number of papers that are devoted to the AOA modeling, the method of fitting models to the environment is not presented in any of the publications. This paper fills this gap. For the assessment of the propagation properties and environment type classification, the basis is the rms delay spread (DS). Therefore, the presented method of the model adaptation to the environment type consists of determining the relationship between the model parameter and DS of environment. Here, the probability density function (PDF) of models such as the modified Gaussian, modified Laplacian, modified logistic, and von Mises distribution are considered as the statistical models of azimuth AOA. For seven different propagation environments, the measurement results are used as a reference data. A comparative analysis shows that the modified Laplacian PDF provides the smallest error fit to measurement data. However, in theoretical analysis and simulation studies, other empirical models can be used due to relatively low approximation errors. The presented results are the basis for the adaptation error assessment of the empirical model for any of the research scenario.

Model of shipping noise in the deep water: Directional density and spatial coherence functions

The shipping noise properties in the deep ocean are studied. Shipping noise exhibits the strong dual-horned directionality features in the flat-seabed ocean, and its directional density can be modeled by a Von Mises distribution. With the explicit expression for the directional density function, the spatial coherence functions of shipping noise are also derived, and the relative features are studied. The research result shows that the properties of shipping noise are different from the ambient noise of other sources, and it can be used for the sonar array design. The model is well matched with the experimental result, and it can be extended to the situations when the ambient noise exhibits the dual-horned structure.