lmomco (version 2.3.7)

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, ...)

Value

An R

vector is returned.

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.

Author

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, pp.f, pp.median

Examples

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)