UKFE (version 1.0.2)

Kappa3AM: Kappa3 distribution - estimates directly from sample

Description

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

Usage

Kappa3AM(x, RP = 100, q = NULL)

Value

quantile as a function of RP or vice versa.

Arguments

x

numeric vector (block maxima sample)

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 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 is the Kappa3 distribution as defined in Kjeldsen, T. (2019), 'The 3-parameter Kappa distribution as an alternative for use with FEH pooling groups.' (Circulation - The Newsletter of the British Hydrological Society, no. 142).

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 an annual maximum sample and estimate the 50-year RP
am_27090 <- GetAM(27090)
Kappa3AM(am_27090$Flow, RP = 50)

# Estimate the RP for a 600 m^3/s discharge
Kappa3AM(am_27090$Flow, q = 600)