likelihood.gradient.augmented: Calculated the gradient of the augmented negative log...

In philmu/climex: Estimating Extreme Events in Climatic Time Series (using Data of the DWD)

Calculated the gradient of the augmented negative log likelihood of the GEV or GP function.

Description

This function uses the likelihood.gradient function and adds the linear constraints used in fit.gev and fit.gpd to produce the augmented Lagrangian version of the GEV or GP negative log-likelihood function.

Usage

likelihood.gradient.augmented(parameters, x.in, model = c("gev", "gpd"),
  lagrangian.multiplier = rep(0, length(x.in) + 2),
  penalty.parameter = 1000)

Arguments

parameters	Numerical vector containing the location, scale, and shape parameters for the GEV or the scale and shape parameters for the GP. If NULL, likelihood.initials is used to determine them. Default = NULL
x.in	Time series of class xts.
model	String determining whether to calculate the initial parameters of the GEV ("gev") or GP ("gpd") function. Default = "gev".
lagrangian.multiplier	Lagrangian multipliers used to weight the linear contribution of the constraints. In most cases all of them are zero, since optimization of the GEV/GP likelihood usually doesn't take place inside a region of constraint violations. When supplying this parameter it has to have the same length as present number of constraints: number of points in x.in + 2, with the last two constraints handling the lower bound of the scale and the shape parameter. Default = 0 for all constraints.
penalty.parameter	Penalty parameter used to weight the quadratic contribution of the constraints. In the end of a typical constrained GEV or GP optimization this parameter is 1000. Default = 1000.

Details

A convenience function not used by the fitting routines.

It is only meant to work with constant parameters and no covariates.

Value

Numerical value of the gradient of the augmented negative log likelihood.

Author(s)

Philipp Mueller

See Also

Other optimization: fit.gev.default, fit.gev.list, fit.gev.xts, fit.gev, fit.gpd.default, fit.gpd.list, fit.gpd.xts, fit.gpd, likelihood.augmented, likelihood.gradient, likelihood.initials, likelihood

philmu/climex documentation built on July 11, 2022, 3:23 p.m.