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In this paper, a new transformed Semicircular Exponentiated Weibull ( SEW ) distribution of three parameters is constructed by applying the transformation of the inverse stereographic projection that maps a real line to the unit circle. The cumulative distribution function, probability density function, expanded probability density function, and reliability measures are presented. Furthermore, the most important statistical aspects of this new distribution, such as moments, trigonometric moments, characteristic function, simulated data, quantile function, reliability stress strength model, Shannon entropy, and relative entropy are obtained. The maximum likelihood estimation method is implemented to estimate the unknown three parameters. A simulation study is conducted to detect empirically the behaviors of the maximum likelihood estimates of the SEW parameters for different default values of the parameters and different samples size.

Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi-dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on ℝ with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all-important location and scale parameters. One important and useful family is comprised of the 'skew-symmetric' distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call 'transformation of scale'—including two-piece distributions—and by probability integral transformation of nonuniform random variables. I also treat briefly the issues of multi-variate extension, of distributions on subsets of ℝ and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal.

In this article, the circular (wrapped) version of Lindley-exponential (WRLE) distribution was introduced, and its different distributional, statistical, and mathematical properties were studied. The maximum likelihood method was used to estimate the model parameters. Simulation results were used to investigate the performance of the estimates. The importance of the proposed distribution was illustrated over: wrapped Lindley, wrapped exponential, new wrapped exponential, and the wrapped xgamma distributions by means of real directional data set.

Scientific flood season segmentation serves as the foundation for determining the flood-limited operating water levels across different periods, providing crucial support for reservoir flood control safety operations and optimal water resource utilization. Under the background of climate change, the traditional static flood-limited water level management model based on fixed dates struggles to adapt to variations in flood season patterns. This study aims to establish a scientifically sound flood season segmentation scheme, providing a basis for dynamic control of flood-limited water levels across different periods, thereby improving water resource utilization efficiency while ensuring flood control safety. This study focuses on the Wuluwati Reservoir and employs the circular distribution method and the Fisher optimal partition method to conduct its flood season segmentation calculations. First, the circular distribution method is used to analyse the concentration and periodic characteristics of flood occurrences in the basin. Subsequently, the Fisher optimal partition method is applied to perform statistical segmentation of the historical hydrological series. Based on this analysis, the flood season of the Wuluwati Reservoir is comprehensively determined as: the pre-flood season from 1 June to 2 July, the main flood season from 3 July to 27 August, and the post-flood season from 28 August to 30 September. To objectively evaluate the rationality of the segmentation results, the improved Cunderlik method was employed to examine the rationality of 15 segmentation schemes based on relative superiority degree. The results show that the scheme with the main flood season from 3 July to 23 August achieves the highest relative superiority degree (0.930). The comprehensively determined segmentation of this study (3 July–27 August) encompasses this optimal interval, demonstrating that the flood season segmentation for the Wuluwati Reservoir is reasonable and effective.

This article proposes an approach, based on infinite Fourier series, to constructing tractable densities for the bivariate circular analogues of copulas recently coined ‘circulas’. As examples of the general approach, we consider circula densities generated by various patterns of nonzero Fourier coefficients. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. The special cases of the circula densities we consider all have simple closed-form expressions involving no computationally demanding normalizing constants and display wide-ranging distributional shapes. A highly successful model identification tool and methods for parameter estimation and goodness-of-fit testing are provided for the circula densities themselves and the bivariate circular densities obtained from them using a marginal specification construction. The modelling capabilities of such bivariate circular densities are compared with those of five existing models in a numerical experiment, and their application illustrated in an analysis of wind directions.

Spatial patterns of movement are fundamental to the ecology of animal populations, influencing their social organization, mating systems, demography, and the spatial distribution of prey and competitors. However, our ability to understand the causes and consequences of animal home range patterns has been limited by the descriptive nature of the statistical models used to analyze them. InMechanistic Home Range Analysis, Paul Moorcroft and Mark Lewis develop a radically new framework for studying animal home range patterns based on the analysis of correlated random work models for individual movement behavior. They use this framework to develop a series of mechanistic home range models for carnivore populations. The authors' analysis illustrates how, in contrast to traditional statistical home range models that merely describe pattern, mechanistic home range models can be used to discover the underlying ecological determinants of home range patterns observed in populations, make accurate predictions about how spatial distributions of home ranges will change following environmental or demographic disturbance, and analyze the functional significance of the movement strategies of individuals that give rise to observed patterns of space use. By providing researchers and graduate students of ecology and wildlife biology with a more illuminating way to analyze animal movement,Mechanistic Home Range Analysiswill be an indispensable reference for years to come.

The logistics of parts entering the factory is an important component of the cost source for manufacturing plants. How to efficiently transport is the key for its enterprises to achieve low-cost control. To address this issue, this study proposed a path planning model based on an improved genetic algorithm. Firstly, a circular distribution model suitable for component transportation logistics was selected, and then constraints such as maximum inventory at the line edge were introduced for design. The basic design of the genetic algorithm was also carried out. Subsequently, three neighborhood structures were introduced for optimization to address the convergence speed and other issues of the algorithm. In response to the demand fluctuation phenomenon in practical applications, a new coding design was carried out. To verify the impact of the model on inbound logistics costs, simulation experiments were conducted on the MATLAB platform. The results showed that the designed algorithm had an average decrease of 14% in total mileage compared to single objective nonlinear models and collaborative network models, while the total cost had decreased by 26.58%. In summary, the improved genetic algorithm model designed in this study has a positive impact on the cost control of inbound logistics.

We propose a five-parameter bivariate wrapped Cauchy distribution as a unimodal model for toroidal data. It is highly tractable, displays numerous desirable properties, including marginal and conditional distributions that are all wrapped Cauchy, and arises as an appealing submodel of a six-parameter distribution obtained by applying Möbius transformation to a pre-existing bivariate circular model. Method of moments and maximum likelihood estimation of its parameters are fast, and tests for independence and goodness-of-fit are available. An analysis involving dihedral angles of the proteinogenic amino acid Tyrosine illustrates the distribution's application. A Markov process for circular data is also explored.

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.

Automated Tape Placement (ATP) technology is one of the processes that is used for the production of the thermoplastic composite materials. The ATP process is complex, requiring multiple melting/crystallization cycles. In the current paper, laser-assisted ATP was used to manufacture two thermoplastic composites (IM7/PEEK and AS4/PA12). Those specimens were compared to specimens that were made of thermoset polymeric composites (IM7/8552) manufactured while using a standard autoclave cycle. In order assess the quality, void content, fibre distribution, and fibre misalignment were measured. After manufacturing, specimens from the three materials were assessed using optical microscopy and computed tomography (CT) scans. The results showed that, as compared to the thermoset composites, thermoplastics that are manufactured by the ATP have a higher amount of voids. On the other hand, manufacturing using the ATP showed an improvement in both the fibre distribution inside the matrix and the fibre misalignment.