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 79 articles )

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  1. 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)
  2. Yanushkevichiene, Olga; Saenko, Viacheslav: Estimation of the characteristic exponent of stable laws (2017)
  3. Li, Xingjie; Williams, Matthew O.; Kevrekidis, Ioannis G.; Menon, Govind: Coarse graining, dynamic renormalization and the kinetic theory of shock clustering (2016)
  4. Ortobelli Lozza, Sergio; Lando, Tommaso; Petronio, Filomena; Tichý, Tomáš: Asymptotic multivariate dominance: a financial application (2016)
  5. Ortobelli, Sergio; Lando, Tommaso; Petronio, Filomena; Tichý, Tomas: Asymptotic stochastic dominance rules for sums of i.i.d. random variables (2016)
  6. Schlägel, Ulrike E.; Lewis, Mark A.: A framework for analyzing the robustness of movement models to variable step discretization (2016)
  7. Tsionas, Mike G.: Bayesian analysis of multivariate stable distributions using one-dimensional projections (2016)
  8. Bandi, Chaithanya; Bertsimas, Dimitris; Youssef, Nataly: Robust queueing theory (2015)
  9. Pogány, Tibor K.; Nadarajah, Saralees: Remarks on the stable $S_\alpha(\beta, \gamma, \mu)$ distribution (2015)
  10. Robinson, G.K.: Practical computing for finite moment log-stable distributions to model financial risk (2015)
  11. Sciacchitano, Federica; Dong, Yiqiu; Zeng, Tieyong: Variational approach for restoring blurred images with Cauchy noise (2015)
  12. Thompson, W.F.; Kuske, R.A.; Monahan, A.H.: Stochastic averaging of dynamical systems with multiple time scales forced with $\alpha$-stable noise (2015)
  13. Bandi, Chaithanya; Bertsimas, Dimitris: Robust option pricing (2014)
  14. Battey, Heather; Linton, Oliver: Nonparametric estimation of multivariate elliptic densities via finite mixture sieves (2014)
  15. Blake, David; Caulfield, Tristan; Ioannidis, Christos; Tonks, Ian: Improved inference in the evaluation of mutual fund performance using panel bootstrap methods (2014)
  16. Cui, Yunwei; Fisher, Thomas J.; Wu, Rongning: Diagnostic tests for non-causal time series with infinite variance (2014)
  17. Devroye, Luc; James, Lancelot: On simulation and properties of the stable law (2014)
  18. El-Hafsi, Boukhalfa: Average sample number function for Pareto heavy tailed distributions (2013)
  19. Fulger, Daniel; Scalas, Enrico; Germano, Guido: Random numbers from the tails of probability distributions using the transformation method (2013)
  20. Ihlen, Espen A.F.: The influence of power law distributions on long-range trial dependency of response times (2013)

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