upstab function

upstab

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).

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

Returns

a numeric value

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.

Author(s)

Mahdi Teimouri, Adel Mohammadpour, and Saralees Nadarajah

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.

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)