pp | R Documentation |

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).

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

`x` |
A vector of data values. The vector is used to get sample size through |

`A` |
A value for the plotting-position coefficient |

`B` |
A value for the plotting-position coefficient |

`a` |
A value for the plotting-position formula from which |

`sort` |
A logical whether the ranks of the data are sorted prior to |

`ties.method` |
This is the argument of the same name passed to |

`...` |
Additional arguments to pass. |

An **R** `vector`

is returned.

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 (see discussion in`pp.f`

).- Median
`a=0.3175`

, Median exceedance probabilities for all distributions (if so, see`pp.median`

).- 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 **R** `rank`

function, which has specific settings to handle tied data. For implementation here, the `ties.method="first"`

method to `rank`

is used. The user has flexibility in changing this to their own custom purposes.

W.H. Asquith

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.

`nonexceeds`

, `pwm.pp`

, `pp.f`

, `pp.median`

, `headrick.sheng.lalpha`

```
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)
```

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