| pp {lmomco} | R Documentation |
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)).
pp(x,a=0)
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 |
An R vector is returned.
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 |
W.H. Asquith
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.
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))