dbgpd_philog: internal

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

Description

internal use only

Usage

dbgpd_philog(x, y, mar1 = c(0, 1, 0.1), mar2 = c(0, 1, 0.1), dep = 2, asy = 0, p = 2, compare = 2, ...)

Arguments

x
y
mar1
mar2
dep
asy
p
compare
...

Details

internal use only

Value

internal use only

Note

internal use only

Author(s)

P. Rakonczai

References

internal use only

See Also

internal use only

Examples

##---- 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, 
    asy = 0, p = 2, compare = 2, ...) 
{
    A1 = expression((x^alpha + (1 - x)^alpha)^(1/alpha))
    fi1 = expression(t + ((64 * a * (c^5 - c^4 - 2 * c^3 - 2 * 
        c^2 + 5 * c - 2) * c^5)/((c + 1)^2 * (c - 1)^2 * (-1 + 
        2 * c) * (1 + 2 * c^2 - 3 * c))) * t^6 + (-32 * a * (5 * 
        c^6 - 2 * c^5 - 13 * c^4 - 12 * c^3 + 15 * c^2 + 6 * 
        c - 6) * c^4/((c + 1)^2 * (c - 1)^2 * (-1 + 2 * c) * 
        (1 + 2 * c^2 - 3 * c))) * t^5 + (32 * c^3 * a * (4 * 
        c^7 + 3 * c^6 - 14 * c^5 - 15 * c^4 + 23 * c^2 - 8 * 
        c - 2)/((c + 1)^2 * (c - 1)^2 * (-1 + 2 * c) * (1 + 2 * 
        c^2 - 3 * c))) * t^4 + (-(32 * (c^7 + 4 * c^6 - 5 * c^5 - 
        10 * c^4 - 5 * c^3 + 12 * c^2 + 2 * c - 4)) * a * c^3/((1 + 
        2 * c^2 - 3 * c) * (c + 1)^2 * (4 * c - 1 + 2 * c^3 - 
        5 * c^2))) * t^3 + ((32 * c^3 * a * (c^6 - 3 * c^4 - 
        c^2 + 4 * c - 2))/((1 + 2 * c^2 - 3 * c) * (c + 1)^2 * 
        (4 * c - 1 + 2 * c^3 - 5 * c^2))) * t^2)
    d1A1 = D(A1, "x")
    d2A1 = D(d1A1, "x")
    A = function(x, alpha) eval({
        x <- x
        alpha <- alpha
        A1
    })
    d1A = function(x, alpha) eval({
        x <- x
        alpha <- alpha
        d1A1
    })
    d2A = function(x, alpha) eval({
        x <- x
        alpha <- alpha
        d2A1
    })
    d1fi1 = D(fi1, "t")
    d2fi1 = D(d1fi1, "t")
    fi = function(t, a, c) eval({
        t <- t
        c <- c
        a <- a
        fi1
    })
    d1fi = function(t, a, c) eval({
        t <- t
        c <- c
        a <- a
        d1fi1
    })
    d2fi = function(t, a, c) eval({
        t <- t
        c <- c
        a <- a
        d2fi1
    })
    Afi = function(t, alpha, a, c) A(fi(t, a, c), alpha)
    d1Afi = function(t, alpha, a, c) d1A(fi(t, a, c), alpha) * 
        d1fi(t, a, c)
    d2Afi = function(t, alpha, a, c) d2A(fi(t, a, c), alpha) * 
        (d1fi(t, a, c))^2 + d1A(fi(t, a, c), alpha) * d2fi(t, 
        a, c)
    mu = function(x, y, alpha, a, c) (1/x + 1/y) * Afi(x/(x + 
        y), alpha, a, c)
    param = as.numeric(c(mar1, mar2, dep, asy, p))
    mux = param[1]
    muy = param[4]
    sigx = param[2]
    sigy = param[5]
    gamx = param[3]
    gamy = param[6]
    alpha = param[7]
    asy = param[8]
    p = param[9]
    hxy = NULL
    error = FALSE
    xx = seq(0, 1, 0.005)
    if (F) {
        par(mfrow = c(1, 2))
        fixx = fi(xx, asy, p) - xx
        plot(xx, fixx, t = "l", ylim = c(min(fixx), max(fixx)), 
            xlab = "t", ylab = expression(phi(t) - t), main = "")
        fipoints(asy, p)
        d2Axx = d2Afi(xx, alpha, asy, p)
        plot(xx, d2Axx, t = "l", ylim = c(-1, max(d2Axx)), xlab = "t", 
            ylab = "A''(t)", main = "")
        abline(h = 0, lty = 2)
    }
    if (min(d2Afi(xx, alpha, asy, p), na.rm = TRUE) < -2.220447e-16) 
        error = TRUE
    if (sigx < 0 | sigy < 0 | alpha < 1.1 | p < 1.3 | p > 5) 
        error = TRUE
    if (!error) {
        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, alpha, asy, p)
        mu1 = tx/(tx + ty)
        dxmu1 = ty/(tx + ty)^2
        dymu1 = (-tx)/(tx + ty)^2
        dxdymu1 = (tx - ty)/(tx + ty)^3
        dxdymu = (-1) * d1Afi(mu1, alpha, asy, p) * (dymu1/tx^2 + 
            dxmu1/ty^2) + (1/tx + 1/ty) * (d2Afi(mu1, alpha, 
            asy, p) * dxmu1 * dymu1 + d1Afi(mu1, alpha, asy, 
            p) * dxdymu1)
        hxy = 1/c0 * dxdymu * dtx * dty
        hxy = as.numeric(hxy * (1 - ((x < 0) * (y < 0))))
        hxy
    }
    else stop("invalid parameter(s)")
    hxy
  }

mgpd documentation built on May 2, 2019, 9:39 a.m.