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, sort=TRUE)

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; and
sort A logical whether the ranks of the data are sorted prior to F computation.

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.

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

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.

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))

# 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)


[Package lmomco version 0.96.3 Index]