Description Usage Arguments Value Note Author(s) References See Also Examples

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.

1 |

`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 |

`...` |
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.

W.H. Asquith

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`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
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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