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#' @include texmexFamily.R
#' @include gpd.info.R
#' @include gpd.sandwich.R
#' @export cgpd
NULL
cgpd <- texmexFamily(name = 'CGPD',
log.lik = function(data, th, ...) {
y <- data$y
X.phi <- data$D$phi
X.eta <- data$D$eta
n.phi <- ncol(X.phi)
n.end <- n.phi + ncol(X.eta)
function(param) {
stopifnot(length(param) == n.end)
phi <- X.phi %*% param[1:n.phi]
eta <- X.eta %*% param[(1 + n.phi):n.end]
sum(dgpd(y, exp(phi), exp(eta) - 1/2, u=th, log.d=TRUE))
}
}, # Close log.lik
param = c(phi=0, eta=exp(.5)),
info = NULL,
sandwich = NULL,
start = function(data){
y <- data$y
X.phi <- data$D[[1]]
X.eta <- data$D[[2]]
c(log(mean(y)), rep(1e-05, -1 + ncol(X.phi) + ncol(X.eta)))
}, # Close start
resid = function(o){
p <- texmexMakeParams(coef(o), o$data$D)
delta <- (o$data$y - o$threshold) / exp(p[,1])
.log1prel(delta * (exp(p[,2]) - 1/2)) * delta # Standard exponential
}, # Close resid
endpoint = function(param, model){
res <- model$threshold - exp(param[, 1]) / (exp(param[, 2]) - 0.5)
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$rate),
exp(param[,1]), exp(param[,2]) - 0.5, u=model$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$rate, param)
out <- matrix(0, nrow=2, ncol=length(m))
if (param[3] == 0){ # exponential case
out[1,] <- exp(param[2]) * log(m * param[1])
} else {
# Next line contains exp(param[2]) because the derivative is of log(sigma), unlike in Coles page 82
out[1,] <- exp(param[2]) / (exp(param[3]) -1/2) * (m * param[1])^((exp(param[3]) - 1/2) - 1)
v <- exp(param[2]) / (exp(param[3]) - 1/2)
u <- ( (m * param[1])^(exp(param[3]) - 1/2) - 1)
dv <- -exp(param[2] + param[3]) / (exp(param[3]) - 1/2)^2
du <- (m * param[1])^(exp(param[3]) - 1/2) * log(m * param[1]) * exp(param[3])
out[2,] <- v * du + u * dv
}
out
}, # Close delta
density = function(n, param, model, log.d = FALSE){
dgpd(n, exp(c(param[, 1])), c(exp(param[, 2]) - 1/2), u=model$threshold, log.d = log.d)
},
rng = function(n, param, model){
rgpd(n, exp(c(param[, 1])), c(exp(param[, 2]) - 1/2), u=model$threshold)
},
prob = function(n, param, model){
pgpd(n, exp(c(param[, 1])), c(exp(param[, 2]) - 1/2), u=model$threshold)
},
quant = function(n, param, model){
qgpd(n, exp(c(param[, 1])), c(exp(param[, 2]) - 1/2), u=model$threshold)
}
)
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