pp {lmomco}R Documentation

Plotting-Position Formula

Description

The plotting positions of a data vector (x) are returned in ascending order. The plotting-position formula is

pp_i = frac{i-a}{n+1-2a} mbox{,}

where pp_i is the nonexceedance probability F of the ith ascending data value. The parameter a specifies the plotting-position type, and n is the sample size (length(x)).

Usage

pp(x,a=0)

Arguments

x A vector of data values. The vector is used to get sample size through length().
a A value for the plotting-position formula. Default is A=0, which returns the Weibull plotting positions

Value

An R vector is returned.

Note

Various plotting positions have been suggested in the literature. Stedinger and others (1992, p. 18.25) comment that "all plotting positions give crude estimates of the unknown [non]exceedance probabilities associated with the largest (and smallest) events." The various plotting positions are summarized in the follow table.

hline Name a Motivation
hline Weibull 0 Unbiased exceedance probability for all distributions
Median 0.3175 Median exceedance probabilities for all distributions
APL about 0.35 Often used with probability-weighted moments
Blom 0.375 Nearly unbiased quantiles for normal distribution
Cunnane 0.40 Approximately quantile unbiased
Gringorten 0.44 Optimized for Gumbel distribution
Hazen 0.50 A traditional choice
hline

Author(s)

W.H. Asquith

References

Stedinger, J.R., Vogel, R.M., and Foufoula-Georgiou, E., 1992, Frequency analysis of extreme events, in Handbook of Hydrology, chapter 18, editor-in-chief D. A. Maidment: McGraw-Hill, New York.

See Also

nonexceeds, pwm.pp

Examples

Q <- rnorm(20)
PP <- pp(Q)
plot(PP,sort(Q))

Q <- rweibull(30,1.4,scale=400)
WEI <- parwei(lmom.ub(Q))
PP <- pp(Q)
plot(PP,sort(Q))
lines(PP,quawei(PP,WEI))

[Package lmomco version 0.92 Index]