Maximum likelihood estimates of point process for the r-largest observations

This uses a constrained optimization routine to return the maximum likelihood estimate based on an n by r matrix of observations. Observations should be ordered, i.e., the r-largest should be in the last column.

Usage

fit.rlarg(
  xdat,
  start = NULL,
  method = c("nlminb", "BFGS"),
  show = FALSE,
  fpar = NULL,
  warnSE = FALSE
)

Arguments

xdat: a numeric vector of data to be fitted.
start: named list of starting values
method: the method to be used. See Details. Can be abbreviated.
show: logical; if TRUE (the default), print details of the fit.
fpar: a named list with fixed parameters, either scale or shape
warnSE: logical; if TRUE, a warning is printed if the standard errors cannot be returned from the observed information matrix when the shape is less than -0.5.

Value

a list containing the following components:

estimate a vector containing all the maximum likelihood estimates.
std.err a vector containing the standard errors.
vcov the variance covariance matrix, obtained as the numerical inverse of the observed information matrix.
method the method used to fit the parameter.
nllh the negative log-likelihood evaluated at the parameter estimate.
convergence components taken from the list returned by auglag. Values other than 0 indicate that the algorithm likely did not converge.
counts components taken from the list returned by auglag.
xdat an n by r matrix of data

Examples

xdat <- rrlarg(n = 10, loc = 0, scale = 1, shape = 0.1, r = 4)
fit.rlarg(xdat)