lmomco (version 2.3.1)

pp: 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 \(i\)th ascending data value. The parameter \(a\) specifies the plotting-position type, and \(n\) is the sample size (length(x)). Alternatively, the plotting positions can be computed by $$pp_i = \frac{i+A}{n+B} \mbox{,}$$ where \(A\) and \(B\) can obviously be expressed in terms of \(a\). The criteria \(A > B > -1\) must be satisfied.

Usage

pp(x, A=NULL, B=NULL, 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 coefficient \(A\).

B

A value for the plotting-position coefficient \(B\).

a

A value for the plotting-position formula from which \(A\) and \(B\) are computed, default is a=0, which returns the Weibull plotting positions.

sort

A logical whether the ranks of the data are sorted prior to \(F\) computation. It was a design mistake years ago to default this function to a sort, but it is now far too late to risk changing the logic now. The function originally lacked the sort argument for many years.

...

Additional arguments to pass.

Value

An R vector is returned.

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, pp.f, pp.median

Examples

# NOT RUN {
Q <- rnorm(20)
PP <- pp(Q)
plot(PP,sort(Q))

Q <- rweibull(30,1.4,scale=400)
WEI <- parwei(lmoms(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)

# }