stable_pdf_and_cdf: PDF and CDF of a skew stable distribution.

In libstableR: Fast and Accurate Evaluation, Random Number Generation and Parameter Estimation of Skew Stable Distributions

Description

Evaluate the PDF or the CDF of the skew stable distribution with parameters pars = c(alpha, beta, sigma, mu) at the points given in x.

parametrization argument specifies the parametrization used for the distribution as described by JP Nolan (1997). The default value is parametrization = 0.

tol sets the relative error tolerance (precision) to tol. The default value is tol = 1e-12.

Usage

stable_pdf(x, pars, parametrization = 0L, tol = 1e-12)

Arguments

x	Vector of points where the pdf will be evaluated.
pars	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.
parametrization	Parametrization used for the skew stable distribution, as defined by JP Nolan (1997). By default, parametrization = 0.
tol	Relative error tolerance (precission) of the calculated values. By default, tol = 1e-12.

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

Nolan JP (1997). Numerical Calculation of Stable Densities and Distribution Functions. Stochastic Models, 13(4) 759-774.

Examples

pars <- c(1.5, 0.9, 1, 0)
x <- seq(-5, 10, 0.001)

pdf <- stable_pdf(x, pars)
cdf <- stable_cdf(x, pars)

plot(x, pdf, type = "l")

Example output

libstableR documentation built on May 2, 2019, 8:49 a.m.