# libstable4u: Fast and accurate evaluation, random number generation and parameter estimation of skew stable distributions. libstable4u provides functions to work with skew stable distributions in a fast and accurate way [1]. It performs: package ## Details * Fast and accurate evaluation of the probability density function (PDF) and cumulative density function (CDF). * Fast and accurate evaluation of the quantile function (inverse CDF). * Random numbers generation [2]. * Skew stable parameter estimation with: * McCulloch's method of quantiles [3]. * Koutrouvellis' method based on the characteristic function [4]. * Maximum likelihood estimation. * Modified maximum likelihood estimation as described in [1]. *The evaluation of the PDF and CDF is based on the formulas provided by John P Nolan in [5]. ## Examples ```r # Set alpha, beta, sigma and mu stable parameters in a vector pars <- c(1.5, 0.9, 1, 0) # Generate an abscissas axis and probabilities vector x <- seq(-5, 10, 0.05) p <- seq(0.01, 0.99, 0.01) # Calculate pdf, cdf and quantiles pdf <- stable_pdf(x, pars) cdf <- stable_cdf(x, pars) xq <- stable_q(p, pars) # Generate random values set.seed(1) rnd <- stable_rnd(100, pars) head(rnd) # Estimate the parameters of the skew stable distribution given # the generated sample: # Using the McCulloch's estimator: pars_init <- stable_fit_init(rnd) # Using the Koutrouvelis' estimator, with McCulloch estimation # as a starting point: pars_est_K <- stable_fit_koutrouvelis(rnd, pars_init) # Using maximum likelihood estimator: pars_est_ML <- stable_fit_mle(rnd, pars_est_K) # Using modified maximum likelihood estimator (see [1]): pars_est_ML2 <- stable_fit_mle2d(rnd, pars_est_K) ``` ## References * [1] Royuela-del-Val J, Simmross-Wattenberg F, Alberola López C (2017). libstable: Fast, Parallel and High-Precision Computation of alpha-stable Distributions in R, C/C++ and MATLAB. Journal of Statistical Software, 78(1), 1-25. doi:10.18637/jss.v078.i01 * [2] Chambers JM, Mallows CL, Stuck BW (1976). A Method for Simulating Stable Random Variables. Journal of the American Statistical Association, 71(354), 340-344. doi:10.1080/01621459.1976.10480344 * [3] McCulloch JH (1986). Simple Consistent Estimators of Stable Distribution Parameters. Communications in Statistics - Simulation and Computation, 15(4), 1109-1136. doi:10.1080/03610918608812563 * [4] Koutrouvelis IA (1981). An Iterative Procedure for the Estimation of the Parameters of Stable Laws. Communications in Statistics - Simulation and Computation, 10(1), 17-28. doi:10.1080/03610918108812189 * [5] Nolan JP (1997). Numerical Calculation of Stable Densities and Distribution Functions. Stochastic Models, 13(4), 759-774. doi:10.1080/15326349708807450 ## Author(s) Javier Royuela del Val, Federico Simmross Wattenberg and Carlos Alberola López; Maintainer: Javier Royuela del Val [jroyval@lpi.tel.uva.es](mailto:jroyval@lpi.tel.uva.es)

libstable4u-package