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

## Description

internal use only

## Usage

 `1` ```pbgpd_taj(x, y, mar1 = c(0, 1, 0.1), mar2 = c(0, 1, 0.1), a = 2, b = 1.5, ...) ```

## Arguments

 `x` `y` `mar1` `mar2` `a` `b` `...`

## 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``` ```##---- 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), a = 2, b = 1.5, ...) { mu = function(x, y) ((1/x)^(2 * a) + 2 * (1 + b) * (1/x/y)^(a) + (1/y)^(2 * a))^(1/2/a) param = as.numeric(c(mar1, mar2, a, b)) mux = param[1] muy = param[4] sigx = param[2] sigy = param[5] gamx = param[3] gamy = param[6] a = param[7] b = param[8] Hxy = NULL error = FALSE if (sigx < 0 | sigy < 0 | a < 1 | b <= -1 | (b > (2 * a - 2))) 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, tx0), pmin(ty, ty0))) } else stop("invalid parameter(s)") Hxy } ```