Fit the GP Distribution {POT} | R Documentation |
Maximum Likelihood, Unbiased Probability Weigthed Moments, Biased Probability Weighted Moments and Moments Estimator to fit Peaks Over a Threshold to a GP distribution.
fitgpd(data, threshold, method, ...)
data |
A numeric vector. |
threshold |
A numeric value giving the threshold for the
GPD. 'mle' method allows varying threshold; so that threshold
could be for this case a numeric vector. Be careful, varying
thresholds are used cyclically if length doesn't match with
data . |
method |
A string giving the names of the estimator. It can be
'mle' , 'moments' , 'pwmu' , 'pwmb' ,
'mdpd' , 'med' and 'pickands' for the maximum
likelihood, moments, unbiased probability weighted moments, biased
probability weigthed moments, minimum density power divergence,
medians and pickands' estimators respectively. |
... |
Other optional arguments to be passed to
gpdmoments , gpdpwmu ,
gpdpwmb and gpdmle , ... functions. |
This function returns a list with composants:
estimate |
A vector containing the maximum likelihood estimates. |
std.err |
A vector containing the standard errors. |
fixed |
A vector containing the parameters of the model that have been held fixed. |
param |
A vector containing all parameters (optimized and fixed). |
deviance |
The deviance at the maximum likelihood estimates. |
corr |
The correlation matrix - for the mle method. |
convergence, counts, message |
Components taken from the
list returned by optim - for the mle method. |
threshold |
The threshold passed to argument threshold . |
nhigh |
The number of exceedences. |
nat, pat |
The number and proportion of exceedences. |
data |
The data passed to the argument data . |
exceedances |
The exceedences, or the maxima of the clusters of exceedences. |
scale |
The scale parameter for the fitted generalized Pareto distribution. |
std.err.type |
The standard error type - for 'mle'
only. That is Observed or Expected Information matrix
of Fisher. |
var.thresh |
Logical. Specify if the threshold is a varying one -
'mle' only. For other methods, threshold is always constant
i.e. var.thresh = FALSE . |
The Maximum Likelihood estimator is obtained through a sligthly
modified version of Alec Stephenson's fpot.norm
function in the
evd
package.
Mathieu Ribatet
Coles, S. (2001) An Introduction to Statistical Modelling of Extreme Values. Springer Series in Statistics. London.
Hosking, J. and Wallis, J. (1987) Parameters and Quantile Estimation for the Generalized Pareto Distribution. Technometrics 29:339–349.
Juarez, S. and Schucany, W. (2004) Robust and Efficient Estimation for the Generalized Pareto Distribution. Extremes 7:237–251.
Peng, L. and Welsh, A. (2001) Robust Estimation of the Generalized Pareto Distribution. Extremes 4:53–65.
Embrechts, P and Klüppelberg, C. and Mikosch, T (1997) Modelling Extremal Events for Insurance and Finance. Springers.
Pickands, J. (1975) Statistical Inference Using Extreme Order Statistics. Annals of Statistics. 3:119–131.
x <- rgpd(200, 1, 2, 0.25) mle <- fitgpd(x, 1, "mle")$param pwmu <- fitgpd(x, 1, "pwmu")$param pwmb <- fitgpd(x, 1, "pwmb")$param pickands <- fitgpd(x, 1, "pickands")$param ##Check if Pickands estimates ##are valid or not !!! med <- fitgpd(x, 1, "med", start = mle)$param ##Sometimes the fitting algo is not ##accurate. So specify ##good starting values is ##a good idea. mdpd <- fitgpd(x, 1, "mdpd")$param print(rbind(mle, pwmu, pwmb, pickands, med, mdpd))