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

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.