stable_fit {libstable4u}

Methods for parameter estimation of skew stable distributions.

Description

A set of functions are provided that perform the parameter estimation of skew stable distributions with different methods.

Usage

stable_fit_init(rnd, parametrization = 0L)

stable_fit_koutrouvelis(rnd, pars_init = as.numeric(c()), parametrization = 0L)

Arguments

rnd

Random sample

parametrization

Parametrization used for the skew stable distribution, as defined by JP Nolan (1997). By default, parametrization = 0.

pars_init

Vector with an initial estimation of the parameters. pars_init = c(alpha, beta, sigma, mu), where

• alpha: shape / stability parameter, with 0 < alpha <= 2.

• beta: skewness parameter, with -1 <= beta <= 1.

• sigma: scale parameter, with 0 < sigma.

• mu: location parameter, with mu real.

Details

• stable_fit_init() uses McCulloch's method of quantiles [3]. This is usually a good initialization for the rest of the methods.

• stable_fit_koutrouvelis() implements Koutrouvellis' method based on the characteristic function [4].

• stable_fit_mle() implements a Maximum likelihood estimation.

• stable_fit_mle2() implements a modified maximum likelihood estimation as described in [1].

Value

A numeric vector.

Author(s)

Javier Royuela del Val, Federico Simmross Wattenberg and Carlos Alberola López

Maintainer: Javier Royuela del Val [e-mail]

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.

Examples

# Set alpha, beta, sigma and mu stable parameters in a vector
pars <- c(1.5, 0.9, 1, 0)

# 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)