# pbgpd_log: internal In mgpd: mgpd: Functions for multivariate generalized Pareto distribution (MGPD of Type II)

## Description

internal use only

## Usage

 `1` ```pbgpd_log(x, y, mar1 = c(0, 1, 0.1), mar2 = c(0, 1, 0.1), dep = 2, ...) ```

## Arguments

 `x` `y` `mar1` `mar2` `dep` `...`

## Details

internal use only

## Value

internal use only

## Note

internal use only

P. Rakonczai

## References

internal use only

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39``` ```##---- Should be DIRECTLY executable !! ---- ##-- ==> Define data, use random, ##-- or do help(data=index) for the standard data sets. ## The function is currently defined as function (x, y, mar1 = c(0, 1, 0.1), mar2 = c(0, 1, 0.1), dep = 2, ...) { mu1 = expression((x^(-alpha) + y^(-alpha))^(1/alpha)) mu = function(x, y) eval({ x <- x y <- y mu1 }) param = as.numeric(c(mar1, mar2, dep)) mux = param[1] muy = param[4] sigx = param[2] sigy = param[5] gamx = param[3] gamy = param[6] alpha = param[7] Hxy = NULL error = FALSE if (sigx < 0 | sigy < 0 | alpha < 1) error = TRUE if (!error) { Hxy = NA tx = (1 + gamx * (x - mux)/sigx)^(1/gamx) ty = (1 + gamy * (y - muy)/sigy)^(1/gamy) tx0 = (1 + gamx * (-mux)/sigx)^(1/gamx) ty0 = (1 + gamy * (-muy)/sigy)^(1/gamy) c0 = -mu(tx0, ty0) Hxy = 1/c0 * (mu(tx, ty) - mu(pmin(tx, rep(tx0, length(tx))), pmin(ty, rep(ty0, length(ty))))) } else stop("invalid parameter(s)") Hxy } ```