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

## Description

internal use only

## Usage

 `1` ```dbgpd_bilog(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``` ```##---- 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, ...) { 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 | a > 1 | b > 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) w = tx/(tx + ty) l = length(w) gma1 = rep(NA, l) for (i in 1:l) { if (!is.na(w[i])) { eqn = function(z) (1 - a) * (1 - w[i]) * (1 - z)^b - (1 - b) * w[i] * z^a if (w[i] == 0) gma1[i] = 0 else if (w[i] == 1) gma1[i] = 1 else gma1[i] <- uniroot(eqn, lower = 0, upper = 1, tol = .Machine\$double.eps^0.5)\$root } } hdens = function(w, gma = gma1) ((1 - a) * (1 - gma) * gma^(1 - a))/((1 - w) * w^2 * ((1 - gma) * a + gma * b)) dxdymu = function(x1, y1) -(x1 + y1)^(-3) * hdens(x1/(x1 + y1)) c0 = log(pbvevd(c(0, 0), model = "bilog", mar1 = c(mux, sigx, gamx), mar2 = c(muy, sigy, gamy), alpha = a, beta = b)) hxy = 1/c0 * dxdymu(tx, ty) * dtx * dty hxy = as.numeric(hxy * (1 - ((x < 0) * (y < 0)))) } else stop("invalid parameter(s)") hxy } ```