fpp {extRemes} | R Documentation |
Fit data to a point process model (allows for covariates in each of the parameters).
fpp(xdat, threshold, npy = 365, ydat = NULL, mul = NULL, sigl = NULL, shl = NULL, mulink = identity, siglink = identity, shlink = identity, show = TRUE, method = "Nelder-Mead", maxit = 10000, ...)
xdat |
'n X 1' vector of observed data. |
threshold |
The threshold; a single number or a numeric 'n X 1' vector. |
npy |
Number of points/observations per year. |
ydat |
Optional 'n X p' matrix of covariate information. |
mul,sigl,shl |
Numeric vectors of integers, giving the columns of 'ydat' that contain covariates for generalized linear modelling of the location, scale and shape parameters repectively (or 'NULL' (the default) if the corresponding parameter is stationary). |
mulink,siglink,shlink |
Inverse link functions for generalized linear modelling of the location, scale and shape parameters repectively. |
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'. |
For non-stationary fitting it is recommended that the covariates within the generalized linear models are (at least approximately) centered and scaled (i.e. the columns of 'ydat' should be approximately centered and scaled).
This function is a modification of the ismev function pp.fit
,
but uses the estimation $sum_i λ_i$ instead of $sum_i λ_icdot I_{x > u}$
(where $λ$ is the exceedance rate and $u$ the threshold) for the rate approximation
of the point process likelihood.
A list containing the following components. A subset of these
components are printed after the fit. If 'show' is 'TRUE', then
assuming that successful convergence is indicated, the components
'nexc', 'nllh', 'mle' and 'se' are always printed.
trans: An logical indicator for a non-stationary fit.
model: A list with components 'mul', 'sigl' and 'shl'.
link: A character vector giving inverse link functions.
threshold: The threshold, or vector of thresholds.
npy: The number of observations per year/block.
nexc: The number of data points above the threshold.
data: The data that lie above the threshold. For non-stationary
models, the data is standardized.
conv: The convergence code, taken from the list returned by
'optim'. A zero indicates successful convergence.
nllh: The negative logarithm of the likelihood evaluated at the
maximum likelihood estimates.
vals: A matrix with four columns containing the maximum likelihood
estimates of the location, scale and shape parameters, and
the threshold, at each data point.
model: A list with components 'mul', 'sigl' and 'shl'.
link: A character vector giving inverse link functions.
threshold: The threshold, or vector of thresholds.
npy: The number of observations per year/block.
nexc: The number of data points above the threshold.
data: The data that lie above the threshold. For non-stationary
models, the data is standardized.
conv: The convergence code, taken from the list returned by
'optim'. A zero indicates successful convergence.
nllh: The negative logarithm of the likelihood evaluated at the
maximum likelihood estimates.
vals: A matrix with four columns containing the maximum likelihood
estimates of the location, scale and shape parameters, and
the threshold, at each data point.
gpd: A matrix with three rows containing the maximum likelihood
estimates of corresponding GPD location, scale and shape
parameters at each data point.
mle: A vector containing the maximum likelihood estimates.
cov: The covariance matrix.
se: A vector containing the standard errors.
Different optimization methods may result in wildly different parameter estimates.
This is adapted from code originally written for S-Plus by Stuart Coles, and ported to R by Alec Stephenson. See details section above.
Eric Gilleland
Beirlant J, Goegebeur Y, Segers J and Teugels J. (2004). Statistics of Extremes, Wiley, Chichester, England.
Coles, Stuart (2001). An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag, London.
pp.fit
, pp.diag
, optim
, pp.fitrange
, mrl.plot
, gpd.fit
# load Fort Collins, CO precipitation dataset. data(FtCoPrec) # Perform a simple point process model fit. x <- FtCoPrec[,"Prec"] fit <- fpp( x, 0.395) pp.diag( fit) # Add seasonal covariates. Time <- FtCoPrec[,"obs"] angle <- (2*pi*Time)/365.25 s <- cbind( sin( angle), cos( angle)) fit <- fpp( xdat=x, threshold=0.395, npy=365.25, ydat=s, mul=1:2, sigl=1:2, siglink=exp) pp.diag( fit)