gpd.pll {mev} | R Documentation |
Profile log-likelihood for the generalized Pareto distribution
Description
This function calculates the (modified) profile likelihood based on the formula.
There are two small-sample corrections that use a proxy for
,
which are based on Severini's (1999) empirical covariance
and the Fraser and Reid tangent exponential model approximation.
Usage
gpd.pll(
psi,
param = c("scale", "shape", "quant", "VaR", "ES", "Nmean", "Nquant"),
mod = "profile",
mle = NULL,
dat,
m = NULL,
N = NULL,
p = NULL,
q = NULL,
correction = TRUE,
threshold = NULL,
plot = TRUE,
...
)
Arguments
psi |
parameter vector over which to profile (unidimensional) |
param |
string indicating the parameter to profile over |
mod |
string indicating the model. See Details. |
mle |
maximum likelihood estimate in |
dat |
sample vector of excesses, unless |
m |
number of observations of interest for return levels. Required only for |
N |
size of block over which to take maxima. Required only for |
p |
tail probability, equivalent to |
q |
level of quantile for N-block maxima. Required only for |
correction |
logical indicating whether to use |
threshold |
numerical threshold above which to fit the generalized Pareto distribution |
plot |
logical; should the profile likelihood be displayed? Default to |
... |
additional arguments such as output from call to |
Details
The three mod
available are profile
(the default), tem
, the tangent exponential model (TEM) approximation and
modif
for the penalized profile likelihood based on approximation proposed by Severini.
For the latter, the penalization is based on the TEM or an empirical covariance adjustment term.
Value
a list with components
-
mle
: maximum likelihood estimate -
psi.max
: maximum profile likelihood estimate -
param
: string indicating the parameter to profile over -
std.error
: standard error ofpsi.max
-
psi
: vector of parametergiven in
psi
-
pll
: values of the profile log likelihood atpsi
-
maxpll
: value of maximum profile log likelihood -
family
: a string indicating "gpd" -
threshold
: value of the threshold, by default zero
In addition, if mod
includes tem
-
normal
: maximum likelihood estimate and standard error of the interest parameter -
r
: values of likelihood root corresponding to -
q
: vector of likelihood modifications -
rstar
: modified likelihood root vector -
rstar.old
: uncorrected modified likelihood root vector -
tem.psimax
: maximum of the tangent exponential model likelihood
In addition, if mod
includes modif
-
tem.mle
: maximum of tangent exponential modified profile log likelihood -
tem.profll
: values of the modified profile log likelihood atpsi
-
tem.maxpll
: value of maximum modified profile log likelihood -
empcov.mle
: maximum of Severini's empirical covariance modified profile log likelihood -
empcov.profll
: values of the modified profile log likelihood atpsi
-
empcov.maxpll
: value of maximum modified profile log likelihood
Examples
## Not run:
dat <- rgp(n = 100, scale = 2, shape = 0.3)
gpd.pll(psi = seq(-0.5, 1, by=0.01), param = 'shape', dat = dat)
gpd.pll(psi = seq(0.1, 5, by=0.1), param = 'scale', dat = dat)
gpd.pll(psi = seq(20, 35, by=0.1), param = 'quant', dat = dat, p = 0.01)
gpd.pll(psi = seq(20, 80, by=0.1), param = 'ES', dat = dat, m = 100)
gpd.pll(psi = seq(15, 100, by=1), param = 'Nmean', N = 100, dat = dat)
gpd.pll(psi = seq(15, 90, by=1), param = 'Nquant', N = 100, dat = dat, q = 0.5)
## End(Not run)