# rbvgpd: Parametric Bivariate GPD In POT: Generalized Pareto Distribution and Peaks Over Threshold

## Description

Density, distribution function and random generation for six different parametric bivariate GPD

## Usage

 ```1 2 3 4``` ```rbvgpd(n, alpha, model = "log", asCoef, asCoef1, asCoef2, mar1 = c(0,1,0), mar2 = mar1) pbvgpd(q, alpha, model = "log", asCoef, asCoef1, asCoef2, mar1 = c(0,1,0), mar2 = mar1, lower.tail = TRUE) ```

## Arguments

 `n` The number of observations to be simulated. `q` A matrix or vector with two columns at which the distribution is computed. `alpha` Dependence parameter for the logistic, asymmetric logistic, negative logistic, asymmetric negative logistic, mixed and asymmetric mixed models. `model` The specified model; a character string. Must be either `"log"` (the default), `"alog"`, `"nlog"`, `"anlog"`, `"mix"` or `"amix"`, for the logistic, asymmetric logistic, negative logistic, asymmetric negative logistic, mixed and asymmetric mixed models respectively. `asCoef,asCoef1,asCoef2` The asymmetric coefficients for the asymmetric logistic, asymmetric negative logistic and asymmetric mixed models. `mar1,mar2` Vectors of length 3 giving the marginal parameters. `lower.tail` Logical. If `TRUE` (the default), P[X <= x] is computed, else P[X >= x].

## Details

The logistic and asymmetric logistic models respectively are simulated using bivariate versions of Algorithms 1.1 and 1.2 in Stephenson(2003). All other models are simulated using a root finding algorithm to simulate from the conditional distributions.

## Value

Generate a random vector of length `n`.

## Author(s)

Mathieu Ribatet (Alec Stephenson for the C codes)

## References

Stephenson, A. G. (2003) Simulating multivariate extreme value distributions of logistic type. Extremes, 6(1), 49–60.

## Examples

 ```1 2 3 4 5 6``` ```x <- rbvgpd(1000, alpha = 0.25, model = "log", mar1 = c(0,1,0.25), mar2 = c(2,0.5, -0.15)) y <- rbvgpd(1000, alpha = 0.75, model = "nlog", mar1 = c(0,1,0.25), mar2 = c(2,0.5, -0.15)) par(mfrow=c(1,2)) plot(x);plot(y) ```

### Example output

```
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POT documentation built on May 2, 2019, 7:30 a.m.