# stable_pdf_and_cdf: PDF and CDF of a skew stable distribution. In libstable4u: Stable Distribution Functions...For You

 stable_pdf_and_cdf R Documentation

## 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 jroyval@lpi.tel.uva.es

### 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")
``````

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