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

## Description

internal use only

## Usage

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

## 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 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61``` ```##---- 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 = 1/2, b = 1/2, ...) { Be1 = function(x) pbeta(x, a + 1, b) Be2 = function(x) pbeta(x, a, b + 1) d1Be1 = function(x) dbeta(x, a + 1, b) d1Be2 = function(x) dbeta(x, a, b + 1) d2 = function(x, a1, b1) x^(a1 - 1) * (a1 - 1) * (1 - x)^(b1 - 1)/(x * beta(a1, b1)) - x^(a1 - 1) * (1 - x)^(b1 - 1) * (b1 - 1)/((1 - x) * beta(a1, b1)) d2Be1 = function(x) d2(x, a + 1, b) d2Be2 = function(x) d2(x, a, b + 1) Qxy = function(x, y) a * 1/y/(a * 1/y + b * 1/x) dxQxy = function(x, y) a * b/(y * (a/y + b/x)^2 * x^2) dyQxy = function(x, y) -a/(y^2 * (a/y + b/x)) + a^2/(y^3 * (a/y + b/x)^2) dxdyQxy = function(x, y) -a * b/(y^2 * (a/y + b/x)^2 * x^2) + 2 * a^2 * b/(y^3 * (a/y + b/x)^3 * x^2) mu = function(x, y) 1/x * (1 - Be1(Qxy(x, y))) + 1/y * Be2(Qxy(x, y)) dxdymu = function(x, y) 1/x^2 * d1Be1(Qxy(x, y)) * dyQxy(x, y) - 1/x * d2Be1(Qxy(x, y)) * dxQxy(x, y) * dyQxy(x, y) - 1/x * d1Be1(Qxy(x, y)) * dxdyQxy(x, y) - 1/y^2 * d1Be2(Qxy(x, y)) * dxQxy(x, y) + 1/y * d2Be2(Qxy(x, y)) * dxQxy(x, y) * dyQxy(x, y) + 1/y * d1Be2(Qxy(x, y)) * dxdyQxy(x, y) 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 < 0 | b < 0) 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 } ```