upstab {alphastable} | R Documentation |

## 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 |

### 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)
```

*alphastable*version 0.2.1 Index]