lmomco (version 2.4.14)

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 \(a\) for \(B > A > -1\) (Hosking and Wallis, 1997, sec. 2.8).

Usage

pp(x, A=NULL, B=NULL, a=0, sort=TRUE, ties.method="first", ...)

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.

ties.method

This is the argument of the same name passed to rank.

...

Additional arguments to pass.

Author

W.H. Asquith

References

Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.

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, headrick.sheng.lalpha

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)