UKFE (version 1.0.2)

GenParetoPOT: Generalised Pareto distribution - estimates directly from sample

Description

Estimated quantiles as function of return period (RP) and vice versa, directly from the data

Usage

GenParetoPOT(x, ppy = 1, RP = 100, q = NULL)

Value

quantile as a function of RP or vice versa

Arguments

x

numeric vector (peaks over threshold sample)

ppy

peaks per year

RP

return period (default = 100)

q

quantile (magnitude of variable)

Author

Anthony Hammond

Details

If the argument q is used, it overrides RP and provides RP as a function of q (magnitude of variable) as opposed to q as a function of RP. The average number of peaks per year argument (ppy) is for the function to convert from the peaks over threshold (POT) scale to the annual scale. For example, if there are 3 peaks per year, the probability associated with the 100-yr return period estimate would be 0.01/3 (i.e. an RP of 300 on the POT scale) rather than 0.01. The parameters are estimated by the method of L-moments, as detailed in 'Hosking J. and Wallis J. 1997 Regional Frequency Analysis: An Approach Based on L-Moments. Cambridge University Press, New York'.

This function applies a probability distribution model which assumes that the sample data is independent and identical, i.e. the assumption is that all observations in the sample would not impact or depend on any other. Furthermore, all observations are from the same underlying process which has not changed over the period of record (stationarity).

Examples

# Get a POT series and estimate the 50-year RP
thames_pot <- POTextract(ThamesPQ[, c(1, 3)], thresh = 0.90)
GenParetoPOT(thames_pot$peak, ppy = 1.867, RP = 50)

# Estimate the RP for a 600 m^3/s discharge
GenParetoPOT(thames_pot$peak, ppy = 1.867, q = 600)