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

## Description

internal use only

## Usage

 `1` ```dbgpd_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 40 41 42 43 44 45 46 47 48 49 50``` ```##---- 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)) dmu1 = D(mu1, "x") ddmu1 = D(dmu1, "y") mu = function(x, y) eval({ x <- x y <- y mu1 }) dxdymu = function(x, y) eval({ x <- x y <- y ddmu1 }) 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) dtx = (1/sigx) * pmax((1 + gamx * (x - mux)/sigx), 0)^(1/gamx - 1) dty = (1/sigy) * pmax((1 + gamy * (y - muy)/sigy), 0)^(1/gamy - 1) c0 = -mu(tx0, ty0) hxy = 1/c0 * dxdymu(tx, ty) * dtx * dty hxy = as.numeric(hxy * (1 - ((x < 0) * (y < 0)))) } else stop("invalid parameter(s)") hxy } ```