gev.hist.fit: Maximum Likelihood Fitting for the GEV distribution in the...

In ilapros/ilaprosUtils: A Miscellaneous Collection of Functions I Tend to Use

Maximum Likelihood Fitting for the GEV distribution in the presence of Historical Data

Description

ML fitting procedures for sample of both systematic and historical data. Function structure inspired by gev.fit in ismev. Arguments naming and likelihood implementation follow Stedinger and Cohn (1986).

Usage

gev.hist.fit(
  xdat,
  k = 0,
  h = NULL,
  X0 = NULL,
  binomialcens = FALSE,
  mulink = identity,
  siglink = identity,
  shlink = identity,
  muinit = NULL,
  siginit = NULL,
  shinit = NULL,
  show = TRUE,
  method = "Nelder-Mead",
  maxit = 10000,
  ...
)

Arguments

xdat	vector of historical and systematic/observed data - the first k elements of the vector should be the historical events
k	number of historical events available. These events should be stored as the first observations of the xdat vector
h	length of years covered by the information of the historical period
X0	the perception threshold which is exceeded by the historical events. This is most likely different from the lowest historical value. It should indicate a value after which we are confident the event would have been recorded or left traces
binomialcens	a logical value. Indicates whether the actual k values are to be used, or if only the information that the threshold X0 has been exceeded is used.
mulink	the link function for the location parameter - default to identity
siglink	the link function for the scale parameter - default to identity
shlink	the link function for the shape parameter - default to identity
muinit	initial values for the location parameter
siginit	initial values for the scale parameter
shinit	initial values for the shape parameter
show	Logical; if TRUE (the default), print details of the fit.
method	The optimization method (see optim for details)
maxit	The maximum number of iterations
...	Other control parameters for the optimization. These are passed to components of the control argument of optim.

Details

The form of the GEV used is that of Coles (2001) Eq (3.2). Specifically, positive values of the shape parameter imply a heavy tail, and negative values imply a bounded upper tail.

Value

An object of the class gev.fit, with additional components related to the historical data.

References

Hosking, J.R.M. and Wallis, J.R., 2005. Regional frequency analysis: an approach based on L-moments. Cambridge university press.

Coles, S., 2001. An introduction to statistical modeling of extreme values. London: Springer.

Stedinger, J.R. and Cohn, T.A., 1986. Flood frequency analysis with historical and paleoflood information. Water resources research, 22(5), pp.785-793.

See Also

glo.hist.fit, dgev, Vignette on historical data

Examples

# check that ismev is installed 
# any(rownames(installed.packages()) == "ismev")
set.seed(5416574)
xx <- rgev(500, 40, 6, -0.2)
xxsist <- xx[471:500]; xxhist <- xx[1:470][xx[1:470] > 80]
gev.hist.fit(c(xxhist,xxsist), k = length(xxhist), h = 470, X0 = 80)
gev.hist.fit(c(xxhist,xxsist), k = length(xxhist), h = 470, X0 = 80, binomialcens = TRUE)
gevd.fit(xxsist) # note the higher standard errors  

ilapros/ilaprosUtils documentation built on April 6, 2023, 4:44 a.m.