wshape
and scale wscale
,
threshold u
and GPD shape xi
and tail
fraction phiu
.dweibullgpdcon(x, wshape = 1, wscale = 1,
u = qweibull(0.9, wshape, wscale), xi = 0, phiu = TRUE,
log = FALSE)
pweibullgpdcon(q, wshape = 1, wscale = 1,
u = qweibull(0.9, wshape, wscale), xi = 0, phiu = TRUE,
lower.tail = TRUE)
qweibullgpdcon(p, wshape = 1, wscale = 1,
u = qweibull(0.9, wshape, wscale), xi = 0, phiu = TRUE,
lower.tail = TRUE)
rweibullgpdcon(n = 1, wshape = 1, wscale = 1,
u = qweibull(0.9, wshape, wscale), xi = 0, phiu = TRUE)
dweibullgpdcon
gives
the density,
pweibullgpdcon
gives
the cumulative distribution function,
qweibullgpdcon
gives
the quantile function and
rweibullgpdcon
gives a
random sample.phiu
permitting a parameterised value
for the tail fraction $\phi_u$. Alternatively, when
phiu=TRUE
the tail fraction is estimated as the
tail fraction from the Weibull bulk model.
The cumulative distribution function with tail fraction
$\phi_u$ defined by the upper tail fraction of the
Weibull bulk model (phiu=TRUE
), upto the threshold
$0 \le x \le u$, given by: pweibull(x, wshape, wscale)
and
pgpd(x, u, sigmau, xi)
).
The cumulative distribution function for pre-specified
$\phi_u$, upto the threshold $0 \le x \le u$, is
given by: dweibull(x, wshape, wscale)
and
dgpd(x, u, sigmau, xi)
). The resulting GPD scale
parameter is then: gpd
for details of GPD upper
tail component and dweibull
for details of Weibull bulk component.gpd
,
dweibull
and
dweibullgpd
Other weibullgpdcon: fweibullgpdcon
,
lweibullgpdcon
,
nlweibullgpdcon
par(mfrow=c(2,2))
x = rweibullgpdcon(1000)
xx = seq(-1, 6, 0.01)
hist(x, breaks = 100, freq = FALSE, xlim = c(-1, 6))
lines(xx, dweibullgpdcon(xx))
# three tail behaviours
plot(xx, pweibullgpdcon(xx), type = "l")
lines(xx, pweibullgpdcon(xx, xi = 0.3), col = "red")
lines(xx, pweibullgpdcon(xx, xi = -0.3), col = "blue")
legend("topleft", paste("xi =",c(0, 0.3, -0.3)),
col=c("black", "red", "blue"), lty = 1)
x = rweibullgpdcon(1000, phiu = 0.2)
hist(x, breaks = 100, freq = FALSE, xlim = c(-1, 6))
lines(xx, dweibullgpdcon(xx, phiu = 0.2))
plot(xx, dweibullgpdcon(xx, xi=0, phiu = 0.2), type = "l")
lines(xx, dweibullgpdcon(xx, xi=-0.2, phiu = 0.2), col = "red")
lines(xx, dweibullgpdcon(xx, xi=0.2, phiu = 0.2), col = "blue")
legend("topleft", c("xi = 0", "xi = 0.2", "xi = -0.2"),
col=c("black", "red", "blue"), lty = 1)
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