This function takes an annual exceedance probability and converts it to a “partial-duration series” (a term in Hydrology) nonexceedance probability through a simple assumption that the Poisson distribution is appropriate for arrive modeling. The relation between the cumulative distribution function \(G(x)\) for the partial-duration series is related to the cumulative distribution function \(F(x)\) of the annual series (data on an annual basis and quite common in Hydrology) by
$$G(x) = [\log(F(x)) + \eta]/\eta\mathrm{.}$$
The core assumption is that successive events in the partial-duration series can be considered as independent. The \(\eta\) term is the arrival rate of the events. For example, suppose that 21 events have occurred in 15 years, then \(\eta = 21/15 = 1.4\) events per year.
A comprehensive demonstration is shown in the example for fpds2f. That function performs the opposite conversion. Lastly, the cross reference to x2xlo is made because the example contained therein provides another demonstration of partial-duration and annual series frequency analysis.
f2fpds(f, rate=NA)A vector of converted nonexceedance probabilities.
A vector of annual nonexceedance probabilities.
The number of events per year.
W.H. Asquith
Stedinger, J.R., Vogel, R.M., Foufoula-Georgiou, E., 1993, Frequency analysis of extreme events: in Handbook of Hydrology, ed. Maidment, D.R., McGraw-Hill, Section 18.6 Partial duration series, mixtures, and censored data, pp. 18.37--18.39.
fpds2f, x2xlo, f2flo, flo2f