Calculation of bivariate cylindrically symmetric α-stable distribution using Wynn’s ε-method. Generated datasets.hdl:21.15109/ARP/BIPBSAARP2024-09-201Sajti, Szilárd Mihály, 2024, "Calculation of bivariate cylindrically symmetric α-stable distribution using Wynn’s ε-method. Generated datasets.", https://hdl.handle.net/21.15109/ARP/BIPBSA, ARP, V1Calculation of bivariate cylindrically symmetric α-stable distribution using Wynn’s ε-method. Generated datasets.hdl:21.15109/ARP/BIPBSASajti, Szilárd MihályARPSajti, Szilárd MihálySajti, Szilárd Mihály2024-09-12Computer and Information ScienceEngineeringMathematical SciencesPhysicsα-stable distributioncorrelation functionnumerical instabilityWynn's ε-methodThe α-stable distributions appear in a broad field. We needed them in X-ray and neutron off-specular scattering, where their characteristic functions are frequently used as correlation functions. In practice, we need the Fourier-transforms of the 2-dimensional (and usually cylindrically symmetric) correlation functions, i.e. the corresponding probability density functions. At first, we used implementations, which we have found sorrily to be numerically unstable. Therefore, we have written a new C++ code using the GNU MPFR (C library for multiple-precision floating-point computations) and boost multiprecision libraries. We present the ‘test’ results generated by this new code here. Additionally, we very shortly summarize the theoretical bases. For further details, we refer the reader to the given references, and the source code and its documentation also are provided.Description.pdfDescription of the datasets, figures, theoretical backgroundapplication/pdfTestStableWynnAlpha06-12.txtBivariate cylindrically symmetric α-stable distribution for values of α in range [0.6, 1.2].text/plainTestStableWynnAlpha12-18.txtBivariate cylindrically symmetric α-stable distribution for values of α in range [1.2, 1.8].text/plainTestStableWynnAlpha18-20.txtBivariate cylindrically symmetric α-stable distribution for values of α in range [0.8, 2.0].text/plainTestStableWynnUAlpha01-02.txtBivariate cylindrically symmetric α-stable distribution for values of α in range [0.1, 0.2].text/plainTestStableWynnUAlpha02-06.txtBivariate cylindrically symmetric α-stable distribution for values of α in range [0.2, 0.6].text/plainTestStableWynnUBoundAlpha01-02.txtRough estimates of convergence boundary points for values of α in range [0.1, 0.2].text/plainTestStableWynnUBoundAlpha02-06.txtRough estimates of convergence boundary points for values of α in range [0.2, 0.6].text/plainAlphaStab01-02U.pngLog-log plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [0.1, 0.2] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnUAlpha01-02.txt.image/pngAlphaStab02-06U.pngLog-log plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [0.2, 0.6] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnUAlpha02-06.txt.image/pngAlphaStab06-12LogB.pngLogarithmic plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [0.6, 1.2] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha06-12.txt.image/pngAlphaStab06-12LogLogB.pngLog-log plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [0.6, 1.2] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha06-12.txt.image/pngAlphaStab06-12Nolan19B.pngBivariate cylindrically symmetric α-stable distribution for values of α in range [0.6, 1.2] calculated based on expression (19) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha06-12.txt.image/pngAlphaStab06-12Nolan21B.pngBivariate cylindrically symmetric α-stable distribution for values of α in range [0.6, 1.2] calculated based on expression (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha06-12.txt.image/pngAlphaStab12-18LogB.pngLogarithmic plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [1.2, 1.8] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha12-18.txt.image/pngAlphaStab12-18LogLogB.pngLog-log plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [1.2, 1.8] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha12-18.txt.image/pngAlphaStab12-18Nolan19B.pngBivariate cylindrically symmetric α-stable distribution for values of α in range [1.2, 1.8] calculated based on expression (19) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha12-18.txt.image/pngAlphaStab12-18Nolan21B.pngBivariate cylindrically symmetric α-stable distribution for values of α in range [1.2, 1.8] calculated based on expression (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha12-18.txt.image/pngAlphaStab18-20LogB.pngLogarithmic plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [1.8, 2.0] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha18-20.txt.image/pngAlphaStab18-20LogLogB.pngLog-Log plot of bivariate cylindrically symmetric α-stable distribution for values of α in range [1.8, 2.0] calculated based on expression (19) and (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha18-20.txt.image/pngAlphaStab18-20Nolan19B.pngBivariate cylindrically symmetric α-stable distribution for values of α in range [1.8, 2.0] calculated based on expression (19) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha18-20.txt.image/pngAlphaStab18-20Nolan21B.pngBivariate cylindrically symmetric α-stable distribution for values of α in range [1.8, 2.0] calculated based on expression (21) of J. P. Nolan Comput. Stat. 28:(5) (2013) 2067–2089. doi: 10.1007/s00180-013-0396-7. It uses the data of the file TestStableWynnAlpha18-20.txt.image/pngAlphaStableDistributionsByWynnsEpsilonMethod.cppC++ file of our algorithm.text/x-c++srcAlphaStableDistributionsByWynnsEpsilonMethod.hC++ header file of our algorithm.text/x-chdrAlphaStableWynnEpsilonSrcDoc.pdfDoxygen generated documentation of the source code of our algorithm.application/pdfCMakeLists.txtCMake project file for the algorithm used for the calculation of bivariate cylindrically symmetric α-stable distribution.text/plainExample.cppExample C++ source file of the usage of our algorithm.text/x-c++srcSumSeriesTerm.hBasic C++ header file of our algorithm defining the classes representing the terms of the series used in our algorithm.text/x-chdrWynnEpsilonMethod.hSource code file of the used implementation of Winn's ε-method.text/x-chdr