gpde {mev} | R Documentation |
Likelihood, score function and information matrix, approximate ancillary statistics and sample space derivative for the generalized Pareto distribution parametrized in terms of expected shortfall.
The parameter m
corresponds to \zeta_u
/(1-\alpha
), where \zeta_u
is the rate of exceedance over the threshold
u
and \alpha
is the percentile of the expected shortfall.
Note that the actual parametrization is in terms of excess expected shortfall, meaning expected shortfall minus threshold.
par |
vector of length 2 containing |
dat |
sample vector |
m |
number of observations of interest for return levels. See Details |
tol |
numerical tolerance for the exponential model |
method |
string indicating whether to use the expected ( |
nobs |
number of observations |
V |
vector calculated by |
The observed information matrix was calculated from the Hessian using symbolic calculus in Sage.
gpde.ll(par, dat, m, tol=1e-5) gpde.ll.optim(par, dat, m, tol=1e-5) gpde.score(par, dat, m) gpde.infomat(par, dat, m, method = c('obs', 'exp'), nobs = length(dat)) gpde.Vfun(par, dat, m) gpde.phi(par, dat, V, m) gpde.dphi(par, dat, V, m)
gpde.ll
: log likelihood
gpde.ll.optim
: negative log likelihood parametrized in terms of log expected
shortfall and shape in order to perform unconstrained optimization
gpde.score
: score vector
gpde.infomat
: observed information matrix for GPD parametrized in terms of rate of expected shortfall and shape
gpde.Vfun
: vector implementing conditioning on approximate ancillary statistics for the TEM
gpde.phi
: canonical parameter in the local exponential family approximation
gpde.dphi
: derivative matrix of the canonical parameter in the local exponential family approximation
Leo Belzile