stable_pdf_and_cdf {libstable4u}

PDF and CDF of a skew stable distribution.

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")