fpp: Point Process

Description

Fit data to a point process model (allows for covariates in each of the parameters).

Usage

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, ...)

Arguments

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

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'.

Details

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). Otherwise, the optimization numerics may be unstable.

This function is a modification of the ismev function pp.fit, but uses the estimation $_i _i$ instead of $_i _iI_{x > u}$ (where $$ 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: A 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. 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. [object Object],[object Object] This is adapted from code originally written for S-Plus by Stuart Coles, and ported to R by Alec Stephenson. See details section above.

Warning

{Different optimization methods may result in wildly different parameter estimates.}

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) misc