Selfdecomposable variables, their background driving distributions(BDDF), log-gamma variables and some graphs

Selfdecomposable variables (distributions) or Lévy class L, arise as a natural generalization of the central limit theorem. It is a quite large class and includes many classical distributions such as stable, gamma, log-gamma, t-Student, logistic, stochastic area under planar Brownian motion, Bessel-K, Bessel densities, Fisher z-distribution, etc. All class L distributions admit the random integral representation - a random integral with respect to some Lévy process Y , called as background driving Lévy process, in short BDLP. Probability distribution of Y(1) is called background driving distribution, in short: BDDF. In the lecture we will present the formulas for BDDF (and for some variables) in a such way that might be more useful for a simulation. References: [1] zjj (2022) Theory Probab. Appl. vol. 67(1), pp. 105-117; [2] zjj (2021) Mathematica Applicanda, vol. 49(2), pp. 85-109.