stable_pdf_and_cdf: PDF and CDF of a skew stable distribution.

In swihart/gnlrim: Generalized Non-Linear Random Intercept Models

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_pdf2(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. For the '2' version, one can have out of bound parameters and an automatic adjustment will be performed to set the parameter to the nearest bound to avoid error message and returning NA.
parametrization	Parametrization used for the skew stable distribution, as defined by JP Nolan (1997). By default, parametrization = 0.
tol	Relative error tolerance (precision) 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

##take out of bound pars and force them in bounds
## ***internally***
pars <- c(2.5, 0.9, 1, 0)
x <- seq(-5, 10, 0.001)

pdf <- stable_pdf2(x, pars)
cdf <- stable_cdf2(x, pars)

## following would error:
## because pars[1] (alpha > 2)
## Not run: 
pdf <- stable_pdf2(x, pars)
cdf <- stable_cdf2(x, pars)

## End(Not run)

swihart/gnlrim documentation built on Oct. 18, 2023, 8:29 p.m.