# R/gpd.R In texmex: Statistical Modelling of Extreme Values

```#' @include texmexFamily.R
#' @include gpd.info.R
#' @include gpd.sandwich.R
#' @export gpd
NULL

gpd <- texmexFamily(name = 'GPD',
log.lik = function(data, th, ...) {
y <- data\$y
X.phi <- data\$D\$phi
X.xi <- data\$D\$xi
n.phi <- ncol(X.phi)
n.end <- n.phi + ncol(X.xi)
function(param) {
stopifnot(length(param) == n.end)
phi <- X.phi %*% param[1:n.phi]
xi <- X.xi %*% param[(1 + n.phi):n.end]
sum(dgpd(y, exp(phi), xi, u=th, log.d=TRUE))
}
}, # Close log.lik
param = c(phi=0, xi=0),
info = gpd.info,
sandwich = gpd.sandwich,
start = function(data){
y <- data\$y
X.phi <- data\$D[[1]]
X.xi <- data\$D[[2]]
c(log(mean(y)), rep(1e-05, -1 + ncol(X.phi) + ncol(X.xi)))
}, # Close start

resid = function(o){
p <- texmexMakeParams(coef(o), o\$data\$D)
delta <- (o\$data\$y - o\$threshold) / exp(p[,1])
.log1prel(delta * p[,2]) * delta # Standard exponential
}, # Close resid

endpoint = function(param, model){
res <- model\$threshold - exp(param[, 1]) / param[, 2]
res[param[, 2] >= 0] <- Inf
res
},
rl = function(m, param, model){
## write in terms of qgpd; let's not reinvent the wheel
qgpd(1/(m * model\$rate),
exp(param[,1]), param[,2], u=model\$threshold,
lower.tail=FALSE)
},
delta = function(param, m, model){
# This is not exact if a prior (penalty) function is used, but
# the CI is approximate anyway.
param <- c(model\$rate, param)
out <- matrix(0, nrow=2, ncol=length(m))
if (param[3] == 0){ # exponential case
out[1,] <- exp(param[2]) * log(m * param[1])
} else {
# Next line contains exp(param[2]) because the derivative is of log(sigma), unlike in Coles page 82
out[1,] <- exp(param[2]) / param[3] * ((m * param[1])^param[3] - 1)
out[2,] <- -exp(param[2]) / (param[3] * param[3]) * ( (m * param[1] )^param[3] - 1 ) +
exp(param[2]) / param[3] * (m * param[1])^param[3] * log(m * param[1])
}
out
}, # Close delta
density = function(n, param, model){
dgpd(n, exp(c(param[, 1])), c(param[, 2]), u=model\$threshold)
},

rng = function(n, param, model){
rgpd(n, exp(c(param[, 1])), c(param[, 2]), u=model\$threshold)
},
prob = function(n, param, model){
pgpd(n, exp(c(param[, 1])), c(param[, 2]), u=model\$threshold)
},
quant = function(n, param, model){
qgpd(n, exp(c(param[, 1])), c(param[, 2]), u=model\$threshold)
}
)
```

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texmex documentation built on May 2, 2019, 5:41 a.m.