Generalized Pareto Distribution Options

Selects information to be displayed and graphs to be plotted after a generalized Pareto distribution has been fitted and controls the type and display of confidence limits.

Note that using profile likelihood confidence limits can be very slow.

Display

This specifies which items of output are to be produced by the analysis.

Model	The formula of the cumulative distribution function for the fitted distribution
Estimates	Parameter estimates of distribution fitted by the analysis
Tests	Goodness of fit tests for the fitted distribution and likelihood ratio tests of the shape parameter (eta)
Fitted values	Produces a table of Observed values from the data and Estimated values from the fitted model
Monitoring	A trace of the log-likelihood and parameters while the optimal values are found

Plot graphs

This specifies which graphs are to be plotted after the analysis. If this is not selected, no graphs will be produced.

Mean residual life	A plot of the mean residual life against the possible thresholds in the data
Parameter stability	A plot of the estimated parameters (eta and sigma) against a range of values of the threshold (all those within the data range)
Cluster size vs threshold	A plot of theta, the reciprocal of the mean cluster size, against a range of values of the threshold
Quantile-quantile	A plot of the sorted data values plotted against the estimated quantiles of the fitted distribution
Probability-probability	A plot of the observed return probabilities plotted against the expected return probabilities from the fitted distribution
Eta profile likelihood	A plot of the profile likelihood obtained by varying the shape parameter, eta, over a range of values, and maximising the log-likelihood over the other parameters for each value of eta. This will provide confidence limits for eta
Density	A combination plot of the observed data values along the x axis, a histogram of the observed values and the fitted probability density function scaled so that the area under the curve equals the area under the histogram
Return levels	A plot of the observed return levels plotted against the expected return period (i.e. 1 in n observations) from the fitted distribution
Return level profile likelihood	A plot of the profile likelihood obtained by varying the return level for the given return probability over a range of values, and maximising the log-likelihood over the other parameters for each value. This will give exact confidence limits for the return levels and is only given if the Exact confidence limits option is selected
Display confidence envelopes	This option puts approximate confidence envelopes/bands around fitted values on any applicable plot at the level specified in the Confidence Level (%) field.

Profile likelihood confidence limits

When selected, the analysis will obtain confidence limits for return levels by forming a profile likelihood over a range of values for the return period. Using exact confidence limits can be very slow, but are more accurate.

When not selected, then approximate quadratic limits will be formed. These are symmetric limits based on the Hessian of the log-likelihood at the maximum-likelihood estimates.

Confidence level (%)

The percentage value of the probability that the confidence limits will contain the true value. Default 95%.

Action buttons

OK	Save the specified options and close the dialog.
Cancel	Close the dialog without making any changes to the options.
Defaults	Set the option settings back to the default settings.