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Journal articles on the topic 'Circular Distribution'

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Published: 7 June 2025

Last updated: 16 July 2025

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Ch, V. Sastry. "Marshall-Olkin Stereographic Circular Logistic Distribution." YMER Digital 21, no. 06 (2022): 664–68. http://dx.doi.org/10.37896/ymer21.06/66.

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Marshall and Olkin (1997) proposed an interesting method of adding a new parameter to the existing distributions. The resulting distributions are called the MarshallOlkin distributions, these distributions include the original distributions as a special case and are more flexible and represent a wide range of behavior than the original distributions. In this paper, a new class of asymmetric stereographic circular logistic distribution is introduced by using Marshall-Olkin transformation on stereographic circular logistic distribution (Dattatreyarao et al (2016)), named as Marshall-Olkin Stereographic Circular Logistic Distribution. The proposed model admits closed form density and distribution functions, generalizes the stereographic circular logistic model and is more flexible to model various types of data (symmetric and skew-symmetric circular data). Keywords:Characteristics, Stereographic circular logistic distribution, circular data, Marshall-Olkin transformation, l -axial data.

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Sakthivel, K. M., and Alicia Mathew. "A Meaningful Construction of New Circular Distribution for Applications in Geomorphology." Indian Journal Of Science And Technology 18, no. 13 (2025): 1009–22. https://doi.org/10.17485/ijst/v18i13.4008.

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Objectives: This work introduces a novel circular probability distributionthe Double Truncated Wrapped Exponential (DTWE) distribution highlighting the importance of circular statistics with cyclical characteristics contrary to usual linear data. Methods: The DTWE distribution is developed using the principle of truncation on the wrapped exponential distribution, which satisfies the principles of circularity. The properties of the distribution, such as the trigonometric mean, skewness, and kurtosis, are derived to enhance interpretability. Parameter estimation is carried out using Maximum Likelihood Estimation, Least Squares, and Weighted Least Squares methods. The goodness-of-fit is carried out, which makes DTWE distribution comparable to other well-known circular probability models. Findings: The numerical results of the simulation study across sample sizes (𝑛 = 30, 50, 100, 1000) and parameter values (𝜃 = 0.5, 1, 2) demonstrate that the DTWE distribution achieves accurate and consistent parameter estimation. For 𝜃 = 0.5 and 𝑛 = 30, the key performance metrics, such as the bias, Mean Square Error (MSE), and standard deviation (SD) for MLE outperform the LS and WLS methods by approximately 20%. Similarly, for 𝜃 = 2 and 𝑛 = 1000, the MLE achieves greater consistency reducing the bias, MSE, and SD by more than 30%. Real world data analysis shows that the DTWE distribution captures the cyclical patterns in ecological and geological data perfectly and gives meaningful insights into directional behaviours. Novelty: This study introduces a novel truncationbased framework for constructing circular probability distributions. The new distribution provides a distinctive approach for evaluating the circular data in ecological and geological datasets. Keywords: Directional Statistics; Truncation; Exponential Distribution; Circular Distribution; MLE

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Girija, S. V. S., A. J. V. Radhika, and A. V. Dattatreya Rao. "On Bimodal Offset Cauchy Distribution." Journal of Applied Mathematics, Statistics and Informatics 9, no. 1 (2013): 61–67. http://dx.doi.org/10.2478/jamsi-2013-0006.

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Abstract The bivariate Cauchy distribution has received applications in many areas, including biological analyses, clinical trials, stochastic modeling of decreasing failure rate life components, study of labour turnover, queuing theory and reliability (Nayak (1987) and Lee and Gross (1991)). In the study of biological analyses, clinical trials and reliability circular distributions will yield suitable results. Circular data arises in a number of different areas such as geological, meteorological, biological and industrial sciences. It is not suggestive to use standard statistical techniques to model circular data, due to the circular geometry of the sample space (p.2 Jammalamadaka and Sen Gupta (2001). It is possible to construct a circular model by transforming a bivariate linear random variate to just its directional component and the resultant model is called ‘offset distribution’. In the literature most of the available circular models were constructed by wrapping a linear model. In recent years some wrapped models were constructed by Dattatreya Rao et al (2007). Here an attempt is made to exploit method of offsetting on Bivariate Cauchy distribution to construct a circular model named by us “OFFSET CAUCHY DISTRIBUTION (OC)”. The characteristic function of the Offset Cauchy model is derived and its characteristics are discussed.

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Sakthivel, K. M., and Alicia Mathew. "MODELLING DIRECTIONAL DATA WITH WRAPPED CHRIS-JERRY DISTRIBUTION IN GEOLOGICAL AND MEDICAL DOMAINS." Advances and Applications in Statistics 92, no. 5 (2025): 683–700. https://doi.org/10.17654/0972361725028.

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In this research, we model a more adaptable paradigm for evaluating circular datasets by creating a new circular distribution by wrapping the Chris-Jerry distribution around the unit circle. The study provides insights into the features of this new circular distribution by examining properties of the wrapped Chris-Jerry distribution, such as means, skewness and kurtosis enhancing our comprehension of circular data patterns. Using maximum likelihood estimate, the distribution parameters have been determined. In order to assess the importance and dominance of the distribution, this is applied to three actual datasets. The relevance of the new distribution is validated by its practical use in real world circumstances, such as evaluating its goodness of fit with actual datasets which shows its consistent performance and reliability in comparison with other distributions.

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K., M. Sakthivel, and Department of Statistics Bharathiar University Coimbatore Tamil Nadu India Professor. "A Meaningful Construction of New Circular Distribution for Applications in Geomorphology." Indian Journal of Science and Technology 18, no. 13 (2025): 1009–22. https://doi.org/10.17485/IJST/v18i13.4008.

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Abstract Objectives: This work introduces a novel circular probability distributionthe Double Truncated Wrapped Exponential (DTWE) distribution highlighting the importance of circular statistics with cyclical characteristics contrary to usual linear data. Methods: The DTWE distribution is developed using the principle of truncation on the wrapped exponential distribution, which satisfies the principles of circularity. The properties of the distribution, such as the trigonometric mean, skewness, and kurtosis, are derived to enhance interpretability. Parameter estimation is carried out using Maximum Likelihood Estimation, Least Squares, and Weighted Least Squares methods. The goodness-of-fit is carried out, which makes DTWE distribution comparable to other well-known circular probability models. Findings: The numerical results of the simulation study across sample sizes (𝑛 = 30, 50, 100, 1000) and parameter values (𝜃 = 0.5, 1, 2) demonstrate that the DTWE distribution achieves accurate and consistent parameter estimation. For 𝜃 = 0.5 and 𝑛 = 30, the key performance metrics, such as the bias, Mean Square Error (MSE), and standard deviation (SD) for MLE outperform the LS and WLS methods by approximately 20%. Similarly, for 𝜃 = 2 and 𝑛 = 1000, the MLE achieves greater consistency reducing the bias, MSE, and SD by more than 30%. Real world data analysis shows that the DTWE distribution captures the cyclical patterns in ecological and geological data perfectly and gives meaningful insights into directional behaviours. Novelty: This study introduces a novel truncationbased framework for constructing circular probability distributions. The new distribution provides a distinctive approach for evaluating the circular data in ecological and geological datasets. Keywords: Directional Statistics; Truncation; Exponential Distribution; Circular Distribution; MLE

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Bell, William, and Saralees Nadarajah. "A Review of Wrapped Distributions for Circular Data." Mathematics 12, no. 16 (2024): 2440. http://dx.doi.org/10.3390/math12162440.

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The wrapped method is the most widely used method for constructing distributions for circular data. In this paper, we provide a review of all known wrapped distributions, including 45 distributions for continuous circular data and 10 distributions for discrete circular data. For each wrapped distribution, we state its nth trigonometric moment, mean direction, mean resultant length, skewness, and kurtosis. We also discuss data applications and limitations of each wrapped distribution. This review could be a useful reference and encourage the development of more wrapped distributions. We also mention an R package available for fitting all of the reviewed distributions and illustrate its applications.

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Phani, Yedlapalli, S.V.S.Girija, Dattatreya Rao A.V., and V. L. N. Srihari G. "Symmetric Circular Model Induced by Inverse Stereographic Projection On Double Weibull Distribution with Application." International Journal of Soft Computing, Mathematics and Control (IJSCMC) 4, no. 1 (2015): 67–74. https://doi.org/10.14810/ijscmc.2015.4106.

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In practical life usually we come across angular or periodic data which needs distributions that are invariant of zero direction and sense of rotation for analysis. Inverse stereographic projection/ Bilinear transformation defined by a one to one mapping generate a class of probability distributions on unit circle that are flexible to analyse circular data. The probability density f unction of many life testing models ranges from 0 to ∞ . Aiming to construct new circular model by applying Inverse Stereographic Projection, we consider Double Weibull distribution and derive density, distribution and characteristic functions of new circular model coined by us Stereographic Double Weibull distribution. Also an attempt is made to study the mathematical aspects in evaluating trigonometric moments of new circular model and present the population characteristics. Goodness of fit to a live data is verified.

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Kim, Sung-Su, and Ashis Sengupta. "Hidden truncation circular normal distribution." Journal of the Korean Data and Information Science Society 23, no. 4 (2012): 797–805. http://dx.doi.org/10.7465/jkdi.2012.23.4.797.

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Nishioka, T., H. Ishizuka, T. Hasegawa, and J. Abe. ""Circular type" quantum key distribution." IEEE Photonics Technology Letters 14, no. 4 (2002): 576–78. http://dx.doi.org/10.1109/68.992616.

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Chaobiao, Wu, and Deng Weicai. "Edgeworth expansion for circular distribution." Applied Mathematics-A Journal of Chinese Universities 11, no. 3 (1996): 295–306. http://dx.doi.org/10.1007/bf02664798.

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Shahsanaei, Fatemeh, and Rahim Chinipardaz. "Sine-Cosine Weighted Circular Distributions." Statistics, Optimization & Information Computing 11, no. 4 (2023): 936–48. http://dx.doi.org/10.19139/soic-2310-5070-1681.

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This paper introduces a new family of multimodal and skew-symmetric circular distributions, namely, the sine-cosine weighted circular distribution. The fundamental properties of this family are examined in the context of a general case and three specific examples. Additionally, general solutions for estimating the parameters of any sine-cosine weighted circular distribution using maximum likelihood are provided. A likelihood-ratio test is performed to check the symmetry of the data. Lastly, two examples are presented that illustrate how the proposed model may be utilized to analyze two real-world case studies with asymmetric datasets.

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Tripsiannis, Gregory A., and Andreas N. Philippou. "Circular Polya distributions of orderk." International Journal of Mathematics and Mathematical Sciences 2003, no. 25 (2003): 1563–75. http://dx.doi.org/10.1155/s0161171203210553.

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Two circular Polya distributions of orderkare derived by means of generalized urn models and by compounding, respectively, the type I and type II circular binomial distributions of orderkof Makri and Philippou (1994) with the beta distribution. It is noted that the above two distributions include, as special cases, new circular hypergeometric, negative hypergeometric, and discrete uniform distributions of the same order and type. The means of the new distributions are obtained and two asymptotic results are established relating them to the above-mentioned circular binomial distributions of orderk.

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Mojtaba, Hatami, and Alamatsaz Hossein. "Transformation of circular random variables based on circular distribution functions." Filomat 32, no. 17 (2018): 5931–47. http://dx.doi.org/10.2298/fil1817931m.

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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.

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Miyata, Yoichi, Takayuki Shiohama, and Toshihiro Abe. "Cylindrical Models Motivated through Extended Sine-Skewed Circular Distributions." Symmetry 16, no. 3 (2024): 295. http://dx.doi.org/10.3390/sym16030295.

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A class of cylindrical distributions, which include the Weibull-von Mises distribution as a special case, is considered. This distribution is obtained by combining the extended sine-skewed wrapped Cauchy distribution (marginal circular part) with the Weibull distribution (conditional linear part). This family of proposed distributions is shown to have simple normalizing constants, easy random number generation methods, explicit moment expressions, and identifiability in parameters. In particular, the marginal distribution of the circular random variable, and its conditional distribution given a linear random variable give relatively stronger skewness than those of existing cylindrical models. Some Monte Carlo simulations and real data analysis are performed to investigate the feasibility and tractability of the proposed models.

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Imoto, Tomoaki, and Toshihiro Abe. "Simple construction of a toroidal distribution from independent circular distributions." Journal of Multivariate Analysis 186 (November 2021): 104799. http://dx.doi.org/10.1016/j.jmva.2021.104799.

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Paula, Fernanda V., Abraão D. C. Nascimento, Getúlio J. A. Amaral, and Gauss M. Cordeiro. "Generalized Cardioid Distributions for Circular Data Analysis." Stats 4, no. 3 (2021): 634–49. http://dx.doi.org/10.3390/stats4030038.

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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.

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Rodríguez, Elio Quiroga. "Golden spiral interferometry for radio astronomy. A proposal." Journal of Instrumentation 19, no. 08 (2024): P08030. http://dx.doi.org/10.1088/1748-0221/19/08/p08030.

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Abstract Radio interferometry is a powerful technique that allows astronomers to create high-resolution images of astronomical objects. The distribution of radio telescopes in an interferometer is a critical factor that determines the resolution and sensitivity of the instrument. Traditionally, radio telescopes are distributed in a linear or circular array. However, recent work has shown that using a golden spiral distribution can improve the resolution and sensitivity of an interferometer. In this paper, the author proposes the use of a golden spiral distribution for radio interferometry, showing that a golden spiral distribution can provide a significant improvement in resolution, up to a factor of eight, compared to a linear or circular distribution. The author also proposes that a golden spiral distribution can improve the sensitivity of an interferometer; it may provide a more uniform distribution of radio telescopes than a linear or circular distribution (a known propety of spiral distributions).

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Wang, Zixin, Yue Jiang, Jialing Liu, Hong Li, and Hao Li. "Experimental Study on Water Distribution and Droplet Kinetic Energy Intensity from Non-Circular Nozzles with Different Aspect Ratios." Agriculture 12, no. 12 (2022): 2133. http://dx.doi.org/10.3390/agriculture12122133.

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(1) Background: In sprinkler irrigation systems, the water distribution and droplet kinetic energy are affected by the shape of the nozzle. In this paper, the effects of working pressure and aspect ratio (L/D) of circular and non-circular nozzles (diamond and ellipse) on water distribution and droplet kinetic energy intensity were investigated; (2) Methods: The hydraulic performance of a PY15 impact sprinkler with circular and non-circular nozzles was assessed under different working pressures, and the droplet diameter, velocity, and kinetic energy intensity were measured by a 2D video disdrometer. Moreover, the coefficient of variation (CV) and form factor (β) were introduced to represent the water distribution and droplet characteristics; (3) Results: The results revealed that, under the same working pressure, the CV of the diamond nozzle was the smallest compared with that of the circular and elliptical nozzles, reflecting a more uniform water distribution. The uniformity of water distribution was the best when the L/D of the elliptical nozzle was the smallest. In general, the larger the outlet diameter, the larger the wetted radius and water application rate. In addition, the smaller the L/D, the smaller the peak water distribution value and the radial increase of the kinetic energy intensity of a single nozzle. The maximum droplet kinetic energy per unit volume of the elliptical nozzle was the smallest compared with that of the circular and diamond nozzles. The circular nozzle at 200 kPa and the diamond and elliptical nozzles at 100 kPa obtained the highest uniformity coefficients of combined kinetic energy intensity distribution, which were 55.93% (circular), 67.59% (diamond), and 57.78% (elliptical) when the combination spacings were 1.0 R, 1.1 R and 1.2 R, and 1.0 R, respectively. Finally, the fitting function of unit volume droplet kinetic energy, distance from the nozzle, L/D, and working pressure of non-circular nozzles was established, and a fitting coefficient of 0.92 was obtained, indicating that the fitting equation was accurate; (4) Conclusions: At low working pressures, the elliptic and diamond nozzles showed better water distributions than the circular nozzle. The distal average droplet diameters of the sprinkler with non-circular nozzles were found to be smaller than those produced by the circular nozzle.

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KURITA, Osamu. "DISTRIBUTION OF CIRCULAR-RADIAL DISTANCE ASSOCIATED WITH CIRCULAR-RADIAL POINT DISTRIBUTIONS : A new application of Crofton's differential equation to circular disk." Journal of Architecture and Planning (Transactions of AIJ) 70, no. 596 (2005): 93–100. http://dx.doi.org/10.3130/aija.70.93_4.

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Gottlieb, H. P. W. "Density Distribution for Isospectral Circular Membranes." SIAM Journal on Applied Mathematics 48, no. 4 (1988): 948–51. http://dx.doi.org/10.1137/0148055.

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Papagiannopoulos, I., G. De Mey, and V. Chatziathanasiou. "Current distribution in circular planar coil." Engineering Analysis with Boundary Elements 37, no. 4 (2013): 747–56. http://dx.doi.org/10.1016/j.enganabound.2013.02.005.

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Nikolayev, Dmitry I., and Tatjana I. Savyolov. "Normal Distribution on the Rotation Group So(3)." Textures and Microstructures 29, no. 3-4 (1997): 201–33. http://dx.doi.org/10.1155/tsm.29.201.

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We study the normal distribution on the rotation group SO(3). If we take as the normal distribution on the rotation group the distribution defined by the central limit theorem in Parthasarathy (1964) rather than the distribution with density analogous to the normal distribution in Eucledian space, then its density will be different from the usual (1/2πσ) exp⁡(−(x−m)2/2σ2) one. Nevertheless, many properties of this distribution will be analogous to the normal distribution in the Eucledian space. It is possible to obtain explicit expressions for density of normal distribution only for special cases. One of these cases is the circular normal distribution.The connection of the circular normal distribution SO(3) group with the fundamental solution of the corresponding diffusion equation is shown. It is proved that convolution of two circular normal distributions is again a distribution of the same type. Some projections of the normal distribution are obtained. These projections coincide with a wrapped normal distribution on the unit circle and with the Perrin distribution on the two-dimensional sphere. In the general case, the normal distribution on SO(3) can be found numerically. Some algorithms for numerical computations are given. These investigations were motivated by the orientation distribution function reproduction problem described in the Appendix.

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Subba Rao, R., V. Ravindranath, A. V.Dattatreya Rao, G. Prasad, and P. Ravi Kishore. "Wrapped Lomax Distribution :a New CircularProbability Model." International Journal of Engineering & Technology 7, no. 3.31 (2018): 150. http://dx.doi.org/10.14419/ijet.v7i3.31.18285.

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Lomax Distribution (Pareto Type IV) is fitted for a life time random variable which can be studied for the data belongs to Actuarialscience, medical diagnosis and Queuing theory etc. In the time of day events observed in cycles like hourly, daily, weekly, monthlyor yearly are in circular distribution. By adopting the technique of wrapping an attempt is made to identify a new circular probabilitymodel originate as Wrapped Lomax Distribution. The concept of circular model is introduced and strategy of wrapping is given forLomaxDistribution. Wrapped Lomax Distribution PDF and CDF are derived, their graphs are also studied. The trigonometric momentsand characteristic function of Wrapped Lomax Distribution are obtained and their graphs are also depicted. The characteristics likemean, variance, skewness, kurtosis and circular standard deviation for various values of location and scale parameters are derived in this paper.

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Abid, Salah Hamza. "The stereographic generalized inverse Weibull distribution." Journal of Physics: Conference Series 2322, no. 1 (2022): 012042. http://dx.doi.org/10.1088/1742-6596/2322/1/012042.

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Abstract When the unit circle is taken as a sample space, the circular data manifest in different aspects of real life. Minh and Farnum (2003) used a stereographic projection to generate new probability distributions on real line [1]. Here, we present an asymmetric distribution called Stereographic generalized inverse Weibull distribution (SGIWD) to represent circular data with focus on the inverse Stereographic Projection. The graph of probability density function is done. We consider here some statistical properties of SGIW distribution, survival and reverse hazard functions, the rth raw moments function, trigonometric moments, stress-strength reliability model, Tsallis, Renyi Shannon entropies and the Kullback–Leibler divergence measure. A simulation study is conducted to evaluate the behavior of the maximum likelihood method to estimate parameters of SGIWD.

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Fernández-Durán, Juan José, and María Mercedes Gregorio-Domínguez. "Sums of Independent Circular Random Variables and Maximum Likelihood Circular Uniformity Tests Based on Nonnegative Trigonometric Sums Distributions." AppliedMath 4, no. 2 (2024): 495–516. http://dx.doi.org/10.3390/appliedmath4020026.

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The sum of independent circular uniformly distributed random variables is also circular uniformly distributed. In this study, it is shown that a family of circular distributions based on nonnegative trigonometric sums (NNTS) is also closed under summation. Given the flexibility of NNTS circular distributions to model multimodality and skewness, these are good candidates for use as alternative models to test for circular uniformity to detect different deviations from the null hypothesis of circular uniformity. The circular uniform distribution is a member of the NNTS family, but in the NNTS parameter space, it corresponds to a point on the boundary of the parameter space, implying that the regularity conditions are not satisfied when the parameters are estimated by using the maximum likelihood method. Two NNTS tests for circular uniformity were developed by considering the standardised maximum likelihood estimator and the generalised likelihood ratio. Given the nonregularity condition, the critical values of the proposed NNTS circular uniformity tests were obtained via simulation and interpolated for any sample size by the fitting of regression models. The validity of the proposed NNTS circular uniformity tests was evaluated by generating NNTS models close to the circular uniformity null hypothesis.

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Lark, R. M., D. Clifford, and C. N. Waters. "Modelling complex geological circular data with the projected normal distribution and mixtures of von Mises distributions." Solid Earth 5, no. 2 (2014): 631–39. http://dx.doi.org/10.5194/se-5-631-2014.

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Abstract. Circular data are commonly encountered in the earth sciences and statistical descriptions and inferences about such data are necessary in structural geology. In this paper we compare two statistical distributions appropriate for complex circular data sets: the mixture of von Mises and the projected normal distribution. We show how the number of components in a mixture of von Mises distribution may be chosen, and how one may choose between the projected normal distribution and the mixture of von Mises for a particular data set. We illustrate these methods with a few structural geological data, showing how the fitted models can complement geological interpretation and permit statistical inference. One of our data sets suggests a special case of the projected normal distribution which we discuss briefly.

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Wang, Jie, Mingyang Wang, and Junlin Tao. "The Effects of Stochastic Circular Pores on Splitting Tensile Behavior of Concrete Based on the Multifractal Theory." Fractal and Fractional 7, no. 7 (2023): 507. http://dx.doi.org/10.3390/fractalfract7070507.

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Concrete naturally contains a large number of circular-like stochastic pores which weaken the tensile strength of concrete and change the crack propagation path. This study investigates the influences of the size distribution and the spatial distribution of stochastic pores on the fracture behavior of concrete based on the splitting tensile test. The mesoscale model of concrete containing coarse aggregate, mortar, interface transition zone (ITZ), and circular pores is established to simulate the crack initiation, propagation, and coalescence of concrete. Concrete samples with a single hole are prepared to verify the effectiveness of the numerical simulation method. Numerical tests are conducted on numerous mesoscale concrete samples with various porosities, pore size distributions, and pore spatial distributions. The numerical simulation results indicate that the tensile strength decreases with the increase of pore size at the same porosity. Based on multifractal theory, a quantitative indicator to describe the spatial distribution uniformity of concrete stochastic pores is proposed. There is a positive correlation between the spatial distribution uniformity of stochastic pores and the tensile strength. The stochastic circular pores can have a profound effect on the concrete’s fracture pattern, which results in three typical macro-crack patterns in the numerical simulation of the splitting tensile test. The presented results deepen the understanding of the influence of stochastic circular pores on the tensile mechanical properties of concrete and provide a reference for the design of concrete structures.

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Rambli, Adzhar, Ibrahim Mohamed, Kunio Shimizu, and Norlina Mohd Ramli. "A Half-Circular Distribution on a Circle." Sains Malaysiana 48, no. 4 (2019): 887–92. http://dx.doi.org/10.17576/jsm-2019-4804-21.

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TOMOZAWA, YUKIO. "THE CMB DIPOLE AND CIRCULAR GALAXY DISTRIBUTION." Modern Physics Letters A 22, no. 21 (2007): 1553–67. http://dx.doi.org/10.1142/s0217732307023936.

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The validity of Hubble's law defies the determination of the center of the big bang expansion, even if it exists. Every point in the expanding universe looks like the center from which the rest of the universe flies away. In this paper, we show that the distri- bution of apparently circular galaxies is not uniform in the sky and that there exists a special direction in the universe in our neighborhood. The data is consistent with the assumption that the tidal force due to the mass distribution around the universe center causes the deformation of galactic shapes depending on its orientation and location relative to the center and our galaxy. Moreover, the CMB dipole data can also be associated with the center of the universe expansion, if the CMB dipole at the center of our supercluster is assumed to be due to Hubble flow. The location of the center is estimated from the CMB dipole data. The direction to the center from both sets of data is consistent and the distance to the center is computed from the CMB dipole data.

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Fimmel, Elena, and Lutz Strüngmann. "Codon Distribution in Error-Detecting Circular Codes." Life 6, no. 1 (2016): 14. http://dx.doi.org/10.3390/life6010014.

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Balachandar, R., and A. S. Ramamurthy. "Pressure Distribution in Cavitating Circular Cylinder Wakes." Journal of Engineering Mechanics 125, no. 3 (1999): 356–58. http://dx.doi.org/10.1061/(asce)0733-9399(1999)125:3(356).

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Bastiaans, Martin J., and Peter G. J. van de Mortel. "Wigner distribution function of a circular aperture." Journal of the Optical Society of America A 13, no. 8 (1996): 1698. http://dx.doi.org/10.1364/josaa.13.001698.

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Kristensson, Gerhard. "The current distribution on a circular disc." Canadian Journal of Physics 63, no. 4 (1985): 507–16. http://dx.doi.org/10.1139/p85-080.

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In this paper we derive the surface-current distribution on a perfectly conducting circular disc. The current is obtained by calculating the limit of the surface currents on an oblate spheroid as the thickness goes to zero. The null-field approach is used. We show that it is possible to calculate all quantities in terms of the spherical basis functions, thus avoiding the cumbersome spheroidal basis functions. Furthermore, it is shown that the correct edge behaviour appears very naturally within the formulation. We compute the surface field on the disc for a plane incident wave, the surface current (eigencurrents) at the complex resonances of the disc, and the induced current on a subterranean disc excited by a circular antenna loop on the ground.

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Xu, Hang, Xinyuan Liu, Yike Ma, et al. "Rotated Object Detection with Circular Gaussian Distribution." Electronics 12, no. 15 (2023): 3265. http://dx.doi.org/10.3390/electronics12153265.

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Rotated object detection is a challenging task due to the difficulties of locating the rotated objects and separating them effectively from the background. For rotated object prediction, researchers have explored numerous regression-based and classification-based approaches to predict a rotation angle. However, both paradigms are constrained by some flaws that make it difficult to accurately predict angles, such as multi-solution and boundary issues, which limits the performance upper bound of detectors. To address these issues, we propose a circular Gaussian distribution (CGD)-based method for angular prediction. We convert the labeled angle into a discrete circular Gaussian distribution spanning a single minimal positive period, and let the model predict the distribution parameters instead of directly regressing or classifying the angle. To improve the overall efficiency of the detection model, we also design a rotated object detector based on CenterNet. Experimental results on various public datasets demonstrated the effectiveness and superior performances of our method. In particular, our approach achieves better results than state-of-the-art competitors, with improvements of 1.92% and 1.04% in terms of AP points on the HRSC2016 and DOTA datasets, respectively.

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Wan, Zhihao, Haifeng Wang, Cheng Huang, et al. "Tight Focusing of Circular Partially Coherent Radially Polarized Circular Airy Vortex Beam." Photonics 10, no. 11 (2023): 1279. http://dx.doi.org/10.3390/photonics10111279.

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The tight focusing properties of circular partially coherent radially polarized circular Airy vortex beams (CPCRPCAVBs) are theoretically studied in this paper. After deriving the cross-spectral density matrix of CPCRPCAVBs in the focal region of a high-NA objective, numerical calculations were performed to indicate the influence of the topological charge of the vortex phase on intensity distribution, degree of coherence and degree of polarization of the tightly focused beam. An intensity profile along the propagation axis shows that a super-length optical needle (~15 λ) can be obtained with a topological charge of 1, and a super-length dark channel (~15 λ) is observed with a topological charge of 2 or 3. In the focal plane, the rise in the number of topological charge does not distort the shapes of the coherence distribution pattern and the polarization distribution pattern, but enlarges their sizes.

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El mokhtari, Karim, Serge Reboul, Georges Stienne, Jean Bernard Choquel, Benaissa Amami, and Mohammed Benjelloun. "An IMM Filter Defined in the Linear-Circular Domain, Application to Maneuver Detection with Heading Only." Mathematical Problems in Engineering 2018 (November 6, 2018): 1–14. http://dx.doi.org/10.1155/2018/3531075.

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In this article, we propose a multimodel filter for circular data. The so-called Circular Interacting Multimodel filter is derived in a Bayesian framework with the circular normal von Mises distribution. The aim of the proposed filter is to obtain the same performance in the circular domain as the classical IMM filter in the linear domain. In our approach, the mixing and fusion stages of the Circular Interacting Multimodel filter are, respectively, defined from the a priori and from the a posteriori circular distributions of the state angle knowing the measurements and according to a set of models. We propose in this article a set of circular models that will be used in order to detect the vehicle maneuvers from heading measurements. The Circular Interacting Multimodel filter performances are assessed on synthetic data and we show on real data a vehicle maneuver detection application.

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Luyun, Chen, and Yi Hong. "Vibration approximate analytical solutions of circular plate consideration of complex pre-stress distribution." Journal of Low Frequency Noise, Vibration and Active Control 39, no. 4 (2019): 987–1001. http://dx.doi.org/10.1177/1461348419852456.

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The influence of the complex pre-stress on the circular plate is investigated herein, with which to solve the non-uniform pre-stress distribution problem. According to the strain–stress equation, the motion differential equations of the circular thin plate with complex pre-stress distribution are derived. Based on the Rayleigh–Ritz theory of energy method, the complex pre-stress distribution function and vibration-displacement function are expanded into the cosine trigonometric series, and the approximate analytical solutions of structural free vibration for circular plate are proposed. A circular plate with simply supported boundary condition, for example, the effectiveness of the proposed method is confirmed through numerical calculations and the finite element method verification. The influence of different type’s distribution of welding residual stress on the natural frequency and mode shape for circular plate structure are compared. The proposed approach in present article can be used in arbitrary pre-stress distribution problem.

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Yovanovich, M. M. "Thermal Resistances of Circular Source on Finite Circular Cylinder With Side and End Cooling." Journal of Electronic Packaging 125, no. 2 (2003): 169–77. http://dx.doi.org/10.1115/1.1568124.

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General solution for thermal spreading and system resistances of a circular source on a finite circular cylinder with uniform side and end cooling is presented. The solution is applicable for a general axisymmetric heat flux distribution which reduces to three important distributions including isoflux and equivalent isothermal flux distributions. The dimensionless system resistance depends on four dimensionless system parameters. It is shown that several special cases presented by many researchers arise directly from the general solution. Tabulated values and correlation equations are presented for several cases where the system resistance depends on one system parameter only. When the cylinder sides are adiabatic, the system resistance is equal to the one-dimensional resistance plus the spreading resistance. When the cylinder is very long and side cooling is small, the general relationship reduces to the case of an extended surface (pin fin) with end cooling and spreading resistance at the base. The special case of an equivalent isothermal circular source on a very thin infinite circular disk is presented.

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Yin, Ke, and Sen Yang. "Study on Bottom Stress Distribution of Circular Foundation on Rock Subgrade." Applied Mechanics and Materials 94-96 (September 2011): 1481–87. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.1481.

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The bottom interaction stress distribution of circular foundation on rock subgrade is generally nonlinear. Different from in soil, it is more complex and have no common conclusion. But it is important for design of this kind foundation. According to the circular foundation’s axial symmetry, using the homogeneous Lame equation in the circular cylindrical coordinates, and the Boussinesq-Galerkin’s general solution, selecting the Love’s strain function as a trial function, the analytic expressions of the bottom stress distribution of the circular foundation on rock subgrade is obtained by the trial Love’s strain function satisfying the boundary conditions. The results of field model tests and numerical simulation analysis are discussed here. It is provided about the bottom interaction stress distribution of circular foundation that is based on rock subgrade by compared the theoretical analysis with the test and numerical calculation. This study conclusion is valuable for design and practice of this foundation engineering.

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Li, Xiuyan, Yangtao Fan, Qingqing Gao, Hu Chen, and Yanhui Liu. "Identification of effects of YOYO-1 intercalation on the topological states of circular DNA." Modern Physics Letters B 32, no. 20 (2018): 1850231. http://dx.doi.org/10.1142/s0217984918502317.

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YOYO-1 intercalation leads to the reduction of twist rigidity, unwinding of DNA, elongation of DNA contour length and YOYO-1 concentration-dependent persistence length, until now few works identified their roles in determining the topological states of circular DNA. Based on the convolution of the writhe distribution of circular DNA obtained by using Monte Carlo simulation and the twist distribution, effects of YOYO-1 intercalation on the linking number distribution of circular DNA are predicted and identified. YOYO-1 intercalation leads to larger fluctuation, but not to the obvious enlargement of the writhe distribution, so that the variance of the linking number distribution mainly depends on the variance of the twist distribution. The unwinding angle contributes to the drifting of the linking number distribution away from the original equilibrium value of zero and has no effects on the variance of the linking number distribution, converse to the roles of the reduced twist rigidity in the linking number distribution. Furthermore, the method used in the work can be generalized to detect the effects of other intercalators on the topological states of circular DNA.

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Teng, Fei, Yun Lin, Yanping Wang, Wenjie Shen, Shanshan Feng, and Wen Hong. "An Anisotropic Scattering Analysis Method Based on the Statistical Properties of Multi-Angular SAR Images." Remote Sensing 12, no. 13 (2020): 2152. http://dx.doi.org/10.3390/rs12132152.

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The scatterings of many targets are aspect dependent, which is called anisotropy. Multi-angular synthetic aperture radar (SAR) is a suitable means of detecting this kind of anisotropic scattering behavior by viewing targets from different aspect angles. First, the statistical properties of anisotropic and isotropic scatterings are studied in this paper. X-band chamber circular SAR data are used. The result shows that isotropic scatterings have stable distributions in different aspect viewing angles while the distributions of anisotropic scatterings are various. Then the statistical properties of single polarization high-resolution multi-angular SAR images are modeled by different distributions. G 0 distribution performs best in all types of areas. An anisotropic scattering analysis method based on the multi-angular statistical properties is proposed. A likelihood ratio test based on G 0 distribution is used to measure the anisotropy. Anisotropic scatterings can be discriminated from isotropic scatterings by thresholding. Besides, the scattering direction can also be estimated by our method. AHH polarization C-band circular SAR data are used to validate our method. The result of using G 0 distribution is compared with the result of using Rayleigh distribution. The result of using G 0 distribution is the better one.

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Lim, T. C. "Circular Auxetic Plates." Journal of Mechanics 29, no. 1 (2012): 121–33. http://dx.doi.org/10.1017/jmech.2012.113.

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AbstractThis paper investigates the suitability of auxetic materials for load-bearing circular plates. It is herein shown that the optimal Poisson's ratio for minimizing the bending stresses is strongly dependent on the final deformed shape, load distribution, and the type of edge supports. Specifically, the use of auxetic material for circular plates is recommended when (a) the plate is bent into a spherical or spherical-like cap, (b) a point load is applied to the center of the plate regardless of the edge conditions, and (c) a uniform load is applied on a simply-supported plate. However, auxetic materials are disadvantaged when a flat plate is to be bent into a saddle-like shell. The optimal Poisson's ratios concept recommended in this paper is useful for providing an added design consideration. In most cases, the use of auxetic materials for laterally loaded circular plates is more advantageous compared to the use of materials with conventional Poisson's ratio, with other factors fixed. This is achieved through materials-based stress re-distribution in addition to the common practices of dimensioning-based stress redistribution and materials strengthening.

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Nguyen, Duy Thao, Duy Hung Vo, and Viet Hai Do. "A Comparison of the Surface Pressure Distribution of Circular Cables and Helical Fillet Cables under Wind Attack: A Wind Tunnel Test Study." Engineering, Technology & Applied Science Research 14, no. 4 (2024): 15393–99. http://dx.doi.org/10.48084/etasr.7602.

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This study examines the aerodynamic performance and surface pressure distribution features of circular and helical fillet stay cables when subjected to wind using wind tunnel testing. The research seeks to clarify the aerodynamic performance disparities between conventional circular stay cables and helical fillet cables, providing valuable insights into their appropriateness for cable-supported structures exposed to wind-induced vibrations. The study initially investigates the aerodynamic efficiency of circular and helical fillet cables. Afterward, the wind tunnel captures the distribution of surface pressure on both cable surfaces. The findings suggest that circular stay cables may undergo cable dry galloping, whereas helical fillet cables demonstrate stability when subjected to wind forces. Furthermore, there are noticeable differences in the surface pressure distribution patterns between circular stay cables and helical fillet cables. Circular stay cables provide a symmetric distribution of pressure, with uniform pressure magnitudes along their surfaces, forming a symmetric pattern. On the other hand, helical fillet cables exhibit modified airflow patterns, leading to asymmetric pressure on the cable surface. Furthermore, the dry galloping observed in circular cables is attributed to the presence of low-frequency components. In contrast, helical fillet cables exhibit a more regulated incidence of low-frequency vortices, making them less prone to wind-induced vibrations.

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Anthony Tyson, J. "Galaxy Mass Distribution from Galaxy-Galaxy Gravitational Lensing." Symposium - International Astronomical Union 117 (1987): 241. http://dx.doi.org/10.1017/s0074180900150259.

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The average gravitational lens distortion of background galaxy images by foreground galaxies is an independent, non-kinematical measurement of galaxy mass distribution M(r)/r (Tyson, et al. 1984). The upper limit we obtained for the equivalent circular velocity, while small compared with some heavy halo models, is consistent with dynamical estimates for samples of galaxies of all types (e.g. Turner's binary data and the Rubin, et al. rotation curves). For example, for a mean cutoff radius of 65 kpc/h, our 3σ upper limit for the equivalent circular velocity (GM/r)1/2 = 190 km/sec. For a mass cutoff at 190 kpc/h our 2σ upper limit is 175 km/sec. If I weight a sample of asymptotical rotation curve velocities by recent field luminosity functions, I get mean circular velocities less than 170 km/sec.

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SenGupta, Ashis, та Moumita Roy. "Circular-Statistics-Based Estimators and Tests for the Index Parameter α of Distributions for High-Volatility Financial Markets". Journal of Risk and Financial Management 16, № 9 (2023): 405. http://dx.doi.org/10.3390/jrfm16090405.

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The distributions for highly volatile financial time-series data are playing an increasingly important role in current financial scenarios and signal analyses. An important characteristic of such a probability distribution is its tail behaviour, determined through its tail thickness. This can be achieved by estimating the index parameter of the corresponding distribution. The normal and Cauchy distributions, and, sometimes, a mixture of the normal and Cauchy distributions, are suitable for modelling such financial data. The family of stable distributions can provide better modelling for such financial data sets. Financial data in high-volatility markets may be better modelled, in many cases, by the Linnik distribution in comparison to the stable distribution. This highly flexible family of distributions is better capable of modelling the inflection points and tail behaviour compared to the other existing models. The estimation of the tail thickness of heavy-tailed financial data is important in the context of modelling. However, the new probability distributions do not admit any closed analytical form of representation. Thus, novel methods need to be developed, as only a few can be found in the literature. Here, we recall a recent novel method, developed by the authors, based on a trigonometric moment estimator using circular distributions. The linear data may be transformed to yield circular data. This transformation is solely for yielding a suitable estimator. Our aim in this paper is to provide a review of the few existing methods, discuss some of their drawbacks, and also provide a universal (∀α∈(0,2]), efficient, and easily implementable estimator of α based on the transformation mentioned above. Novel, circular-statistics-based tests for the index parameter α of the stable and Linnik distributions are introduced and also exemplified with real-life financial data. Two real-life data sets are analysed to exemplify the methods recommended and enhanced by the authors.

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López-Cobá, C., Lihwai Lin, and Sebastián F. Sánchez. "XookSuut: A BAYESIAN TOOL FOR MODELING CIRCULAR AND NON–CIRCULAR FLOWS ON 2D VELOCITY MAPS." Revista Mexicana de Astronomía y Astrofísica 60, no. 1 (2024): 19–39. http://dx.doi.org/10.22201/ia.01851101p.2024.60.01.03.

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We present XookSuut, a Python implementation of the DiskFit algorithm, optimized to perform robust Bayesian inference on parameters describing models of circular and noncircular rotation in galaxies. XookSuut surges as a Bayesian alternative for kinematic modeling of 2D velocity maps; it implements effcient sampling methods, specifically Markov Chain Monte Carlo (MCMC) and Nested Sampling (NS), to obtain the posteriors and marginalized distributions of kinematic models including circular motions, axisymmetric radial ﬂows, bisymmetric ﬂows, and harmonic decomposition of the LoS velocity. In this way, kinematic models are obtained by pure sampling methods, rather than standard minimization techniques based on the Χ2. All together, XookSuut represents a sophisticated tool for deriving rotational curves and to explore the error distribution and covariance between parameters.

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NAKANO, Masahiro, Yugo KAJIO, Masahiro TAKIGUCHI, and Hisao NISHIOKA. "Stress distribution surrounding the circular shaft's cut-out." Doboku Gakkai Ronbunshu, no. 356 (1985): 555–63. http://dx.doi.org/10.2208/jscej.1985.356_555.

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Cascales, Laura, and David J. Craik. "Naturally occurring circular proteins: distribution, biosynthesis and evolution." Organic & Biomolecular Chemistry 8, no. 22 (2010): 5035. http://dx.doi.org/10.1039/c0ob00139b.

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Zinhom, Esmail, Manal Mohamed Nassar, Ayat Elmasry, and Salwa Said Radwan. "Wrapped Exponential Distribution Generalizations for Circular Data Analysis." Journal of the Egyptian Mathematical Society 32, no. 1 (2024): 57–82. https://doi.org/10.21608/joems.2024.309359.1001.

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Yedlapalli, Phanı, Venkata Sesha Girija Sagi, Peddi Raju Cherukuri, and Naveen Venkata Kishore Gajula. "New Circular Distribution with an Application to Biology." Cumhuriyet Science Journal 45, no. 2 (2024): 194–200. http://dx.doi.org/10.17776/csj.1316115.

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In this paper, we introduce a new circular distribution known as the wrapped new weighted exponential distribution (WNWE) is introduced. We derive an explicit expression for its probability density function and establish closed-form expressions for the distribution function, characteristic function, and trigonometric moments. Furthermore, we discuss the properties of the proposed model. We employ the method of maximum likelihood estimation to estimate the parameters. To demonstrate the applicability of the proposed distribution, we analyze a real dataset consisting of 50 starhead top minnows.

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