Calculation of bivariate cylindrically symmetric α-stable distribution using Wynn’s ε-method. Generated datasets. (hdl:21.15109/ARP/BIPBSA)

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Calculation of bivariate cylindrically symmetric α-stable distribution using Wynn’s ε-method. Generated datasets.

hdl:21.15109/ARP/BIPBSA

ARP

2024-09-20

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Sajti, 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, V1

Calculation of bivariate cylindrically symmetric α-stable distribution using Wynn’s ε-method. Generated datasets.

hdl:21.15109/ARP/BIPBSA

Sajti, Szilárd Mihály (Wigner Research Centre for Physics)

ARP

Sajti, Szilárd Mihály

Sajti, Szilárd Mihály

2024-09-12

https://hdl.handle.net/21.15109/ARP/BIPBSA

Computer and Information Science, Engineering, Mathematical Sciences, Physics, α-stable distribution, correlation function, numerical instability, Wynn's ε-method

The 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.

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Description.pdf

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Description of the datasets, figures, theoretical background

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TestStableWynnAlpha06-12.txt

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Bivariate cylindrically symmetric α-stable distribution for values of α in range [0.6, 1.2].

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TestStableWynnAlpha12-18.txt

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Bivariate cylindrically symmetric α-stable distribution for values of α in range [1.2, 1.8].

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TestStableWynnAlpha18-20.txt

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Bivariate cylindrically symmetric α-stable distribution for values of α in range [0.8, 2.0].

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TestStableWynnUAlpha01-02.txt

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Bivariate cylindrically symmetric α-stable distribution for values of α in range [0.1, 0.2].

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TestStableWynnUAlpha02-06.txt

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Bivariate cylindrically symmetric α-stable distribution for values of α in range [0.2, 0.6].

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TestStableWynnUBoundAlpha01-02.txt

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Rough estimates of convergence boundary points for values of α in range [0.1, 0.2].

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TestStableWynnUBoundAlpha02-06.txt

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Rough estimates of convergence boundary points for values of α in range [0.2, 0.6].

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AlphaStab01-02U.png

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Log-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.

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AlphaStab02-06U.png

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Log-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.

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AlphaStab06-12LogB.png

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Logarithmic 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.

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AlphaStab06-12LogLogB.png

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Log-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.

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AlphaStab06-12Nolan19B.png

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Bivariate 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.

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AlphaStab06-12Nolan21B.png

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Bivariate 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.

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AlphaStab12-18LogB.png

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Logarithmic 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.

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AlphaStab12-18LogLogB.png

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Log-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.

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AlphaStab12-18Nolan19B.png

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Bivariate 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.

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AlphaStab12-18Nolan21B.png

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Bivariate 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.

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AlphaStab18-20LogB.png

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Logarithmic 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.

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AlphaStab18-20LogLogB.png

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Log-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.

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AlphaStab18-20Nolan19B.png

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Bivariate 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.

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AlphaStab18-20Nolan21B.png

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Bivariate 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.

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AlphaStableDistributionsByWynnsEpsilonMethod.cpp

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C++ file of our algorithm.

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AlphaStableDistributionsByWynnsEpsilonMethod.h

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C++ header file of our algorithm.

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AlphaStableWynnEpsilonSrcDoc.pdf

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Doxygen generated documentation of the source code of our algorithm.

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CMakeLists.txt

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CMake project file for the algorithm used for the calculation of bivariate cylindrically symmetric α-stable distribution.

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Example.cpp

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Example C++ source file of the usage of our algorithm.

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SumSeriesTerm.h

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Basic C++ header file of our algorithm defining the classes representing the terms of the series used in our algorithm.

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WynnEpsilonMethod.h

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Source code file of the used implementation of Winn's ε-method.

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