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, sort=TRUE)
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; and |
sort |
A logical whether the ranks of the data are sorted prior to F computation. |
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 |
The function uses the rank()
function, which has specific settings to handle tied data. For implementation here, the ties.method="first"
method to rank()
is used.
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)) # This plot looks similar, but when connecting lines are added # the nature of the sorting is obvious. plot(pp(Q,sort=FALSE), Q) lines(pp(Q,sort=FALSE), Q, col=2)