# udstab: udstab In alphastable: Inference for Stable Distribution

## Description

computes the probability density function (pdf) 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

 `1` ```udstab(x, alpha, beta, sigma, mu, param) ```

## Arguments

 `x` point at which the pdf 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

a numeric value

## Note

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

## 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

 ```1 2 3 4``` ```# In the following, we compute the pdf 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. library("stabledist") udstab(2,1.2,0.9,1,0,1) ```

alphastable documentation built on Sept. 11, 2019, 1:04 a.m.