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

A vector of data values. The vector is used to get sample size through length();

A value for the plotting-position coefficient $A$;

A value for the plotting-position coefficient $B$;

A value for the plotting-position formula from which $A$ and $B$ are computed, 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.

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.

Examples

Run this code

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)