stable_pdf_and_cdf: PDF and CDF of a skew stable distribution.

stable_pdf_and_cdfR Documentation

PDF and CDF of a skew stable distribution.


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.


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



Vector of points where the pdf will be evaluated.


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


Relative error tolerance (precission) of the calculated values. By default, tol = 1e-12.


A numeric vector.


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

Maintainer: Javier Royuela del Val


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


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")

libstable4u documentation built on June 22, 2024, 10:50 a.m.