Some Statistics in Polar Coordinate System with Uniform Angles

Objective & Hypothesis:In this study, some bivariate distribution functions are defined in the polar coordinate system andrandom numbers are generated from these distribution functions.

📊

Key Findings & Data:Also, the chi-square goodnessof-fit test is proposed for random numbers generated in the polar coordinates.

💡

Conclusion & Impact:Lastly, the validity and the success of the proposed methodis shown in the simulation study and the real-life example.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Domain Parameters

Abstract

In this study, some bivariate distribution functions are defined in the polar coordinate system andrandom numbers are generated from these distribution functions. In these definitions, the angularchange of the probability density function is taken as constant, and the distance change isperformed based on the univariate probability density function. Also, the chi-square goodnessof-fit test is proposed for random numbers generated in the polar coordinates. Four differentdistribution functions are selected to evaluate the success of the proposed chi-square goodness offit test for polar distribution functions. Lastly, the validity and the success of the proposed methodis shown in the simulation study and the real-life example.

🔖

Cite This Article

TIRYAKI, B. K., PAK, A., TEZEL, O., KESEMEN, O. (2022). Some Statistics in Polar Coordinate System with Uniform Angles. Gazi University Journal of Science, Cilt: 33 - Sayı: 3, 846–882. https://ajindex.com/articles/521253

📄 Full Text PDF Viewer

Open in New Tab ↗

↗New Tab

📄

PDF görüntüleyici hazırlanıyor...

References (14)

Alford, M.H., MacKinnon J.A., Pinkel R. and Klymak J.M., “Space-time scales of shear in the North Pacific”, Journal of Physical Oceanography, 47(10): 2455-2478, (2017).
Solman, G.J., Kingstone, A., “Balancing energetic and cognitive resources: Memory use during search depends on the orienting effector”, Cognition, 132(3): 443-454, (2014).
Schönefeld, J., “Architectures for Embedded Multimodal Sensor Data Fusion Systems in the Robotics -and Airport Traffic Surveillance - Domain”, Phd.Thesis, Clausthal University of Technology, Clausthal-Zellerfeld, 28-35 (2015).
Cumming, B.G., DeAngelis, G.C., “The physiology of stereopsis”, Annual Review of Neuroscience, 24(1): 203-238, (2001).
Robinson, N.H., Newton, H.M, Allan, J.D., Irwin, M., Hamilton, J.F., Flynn, M., Bower, K.N., Williams, P.I., Mills, G., Reeves, C.E., McFiggans, G., and Coe, H., “Source attribution of Bornean air masses by back trajectory analysis during the OP3 project”, Atmospheric Chemistry and Physics, 11(18): 9605-9630, (2011).
Schomaker, L., Bulacu, M., and van Erp, M., “Sparse-parametric writer identification using heterogeneous feature groups”, International Conference on Image Processing, Barcelona, Spain, 545-549 (2003).
Fazio, V.S., Komitov, L., Radüge, C., Lagerwall, S.T., and Motschmann, H., “Influence of the flow on the anchoring of nematic liquid crystals on Langmuir-Blodgett monolayers studied by optical second-harmonic generation”, The European Physical Journal E, 5(3): 309-315, (2001).
Kesemen, O., Tiryaki, B.K., and Tuncay, U., “A Novel Approximation for Computation Bivariate Distribution Functions in Polygonal Area”, 5th International Eurasian Conference on Mathematical Sciences and Applications (IECMSA-2016), Belgrade, 191-191 (2016).
Papoulis, A., Pillai, S.U., Probability, Random Variables, and Stochastic Processes 4th ed., McGraw Hill, New York, (2002).
Ertel, B.R., Reed, H.J., “Angle and time of arrival statistics for circular and elliptical scattering models”, IEEE Journal on Selected Areas in Communications, 17(11): 1829-1840, (1999).
Kreyszig, E., Advanced Engineering Mathematics, John Willey & Sons Inc., New York, (1999).
Pak, A., “Kutupsal Koordinatlarda Ki-Kare ve Kolmogorov-Smirnov Uyum İyiliği Testleri”, MSc. Thesis, Karadeniz Technical University, Trabzon, 19-43 (2017).
Devroye, L., Non-Uniform Random Variate Generation, Springer, New York, (1986). Marques de Sà, J.P., Applied Statistics using SPSS, STATISTICA, MATLAB and R, Springer, New York, (2007).
O'connor, P.