upstab {alphastable}

upstab

Description

computes the cumulative distribution function (cdf) of the univariate stable distribution based on formulas given by Nolan (1997) <doi.org/10.1080/15326349708807450> and asymptotic series, see Teimouri and Amindavar (2008).

Usage

upstab(x, alpha, beta, sigma, mu, param)

Arguments

x

point at which the cdf is computed

alpha

tail index parameter

beta

skewness parameter

sigma

scale parameter

mu

location parameter

param

kind of parameterization; must be 0 or 1 for S_0 and S_1 parameterizations, respectively

Value

a numeric value

Note

upstab() computes the cdf of univariate stable distribution using asymptotic series within their convergence regions. For points outside of convergence regions, the cdf is computed using stabledist package based on formulas given by Nolan (1997). So, to compute the cdf using the upstab() we may need to install stabledist package.

Author(s)

Mahdi Teimouri, Adel Mohammadpour, and Saralees Nadarajah

References

Nolan, J. P. (1997). Numerical calculation of stable densities and distribution functions, Communications in statistics-Stochastic models, 13(4), 759-774.

Teimouri, M. and Amindavar, H. (2008). A novel approach to calculate stable densities, Proceedings of the World Congress on Engineering, 1, 710-714.

Examples

# In the following, we compute the cdf of a univariate stable distribution at point 2
# with parameters alpha=1.2, beta=0.9, sigma=1, and mu=0 in S_{0} parameterization.
upstab(2,1.2,0.9,1,0,1)