The program calculates the density (pdf), cumulative distribution function (cdf), and quantiles for a general stable distribution. These routines are based on the formulas in ”Numerical calculation of stable densities and distribution functions”, J. P. Nolan, Commun. Statist.-Stochastic Models, 13(4), 759-774 (1997). Also included is a version of Chambers, Mallows and Stuck’s algorithm to generate stable random variates. It also performs maximum likelihood estimation of stable parameters and some exploratory data analysis techniques for assessing the fit of a data set. This work is described in the paper ”Maximum likelihood estimation of stable parameters”, J. P. Nolan, in the book Levy Processes, Ed. by Barndorff-Nielsen, Mikosch and Resnick, Birkhauser, 2001 (currently on my webpage).

References in zbMATH (referenced in 107 articles )

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  1. Clément, Emmanuelle; Gloter, Arnaud: Joint estimation for SDE driven by locally stable Lévy processes (2020)
  2. Kakinaka, Shinji; Umeno, Ken: Flexible two-point selection approach for characteristic function-based parameter estimation of stable laws (2020)
  3. Kim, Geonwoo; Cho, Junghee; Kang, Myungjoo: Cauchy noise removal by weighted nuclear norm minimization (2020)
  4. Shi, Kehan; Dong, Gang; Guo, Zhichang: Cauchy noise removal by nonlinear diffusion equations (2020)
  5. Vankov, Emilian R.; Guindani, Michele; Ensor, Katherine B.: Filtering and estimation for a class of stochastic volatility models with intractable likelihoods (2019)
  6. Ament, Sebastian; O’Neil, Michael: Accurate and efficient numerical calculation of stable densities via optimized quadrature and asymptotics (2018)
  7. Balakrishna, N.; Hareesh, G.: Analysis of autoregressive models with symmetric stable innovations (2018)
  8. Calzolari, Giorgio; Halbleib, Roxana: Estimating stable latent factor models by indirect inference (2018)
  9. Crisanto-Neto, J. C.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.: An efficient series approximation for the Lévy (\alpha)-stable symmetric distribution (2018)
  10. Kelly, James F.; Li, Cheng-Gang; Meerschaert, Mark M.: Anomalous diffusion with ballistic scaling: a new fractional derivative (2018)
  11. Mei, Jin-Jin; Dong, Yiqiu; Huang, Ting-Zhu; Yin, Wotao: Cauchy noise removal by nonconvex ADMM with convergence guarantees (2018)
  12. Weron, Aleksander: Mathematical models for dynamics of molecular processes in living biological cells a single particle tracking approach (2018)
  13. Alrawashdeh, Mahmoud S.; Kelly, James F.; Meerschaert, Mark M.; Scheffler, Hans-Peter: Applications of inverse tempered stable subordinators (2017)
  14. Javier Royuela-del-Val and Federico Simmross-Wattenberg and Carlos Alberola-López: libstable: Fast, Parallel, and High-Precision Computation of α-Stable Distributions in R, C/C++, and MATLAB (2017) not zbMATH
  15. Julián-Moreno, Guillermo; López de Vergara, Jorge E.; González, Iván; de Pedro, Luis; Royuela-del-Val, Javier; Simmross-Wattenberg, Federico: Fast parallel (\alpha)-stable distribution function evaluation and parameter estimation using OpenCL in GPGPUs (2017)
  16. Teimouri, Mahdi; Rezakhah, Saeid; Mohammadpour, Adel: (U)-statistic for multivariate stable distributions (2017)
  17. Yanushkevichiene, Olga; Saenko, Viacheslav: Estimation of the characteristic exponent of stable laws (2017)
  18. Gao, Ting; Duan, Jinqiao; Li, Xiaofan: Fokker-Planck equations for stochastic dynamical systems with symmetric Lévy motions (2016)
  19. Koblents, Eugenia; Míguez, Joaquín; Rodríguez, Marco A.; Schmidt, Alexandra M.: A nonlinear population Monte Carlo scheme for the Bayesian estimation of parameters of (\alpha)-stable distributions (2016)
  20. Liang, Yingjie; Chen, Wen; Magin, Richard L.: Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation (2016)

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