# unitpareto: The unit Pareto Distribution In RTDE: Robust Tail Dependence Estimation

## Description

Density function, distribution function, quantile function, random generation.

## Usage

 ```1 2 3 4``` ```dupareto(x, log = FALSE) pupareto(q, lower.tail=TRUE, log.p = FALSE) qupareto(p, lower.tail=TRUE, log.p = FALSE) rupareto(n) ```

## Arguments

 `x, q` vector of quantiles. `p` vector of probabilities. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].

## Details

The extended Pareto distribution is defined by the following density and distribution function

f(x) = 1/x^2, F(x) = 1-1/x,

for all x>0.

## Value

`dupareto` gives the density, `pupareto` gives the distribution function, `qupareto` gives the quantile function, and `rupareto` generates random deviates.

The length of the result is determined by `n` for `rupareto`, and is the maximum of the lengths of the numerical parameters for the other functions.

The numerical parameters other than `n` are recycled to the length of the result. Only the first elements of the logical parameters are used.

## Author(s)

Christophe Dutang

## References

Johnson, N.L., Kotz, S. and Balakrishnan, N. (2000), Continuous Univariate Distributions, Volume 1, Second Edition, John Wiley and Sons.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```##### # (1) density function x <- seq(0, 5, length=24) cbind(x, dupareto(x)) ##### # (2) distribution function cbind(x, pupareto(x)) ```

RTDE documentation built on Jan. 8, 2020, 5:09 p.m.