# pp.f: Quantile Function of the Ranks of Plotting Positions In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

There are two major forms (outside of the general plotting-position formula `pp`) for estimation of the p_rth probability of the rth order statistic for a sample of size n: the mean is pp'_r = r/(n+1) (Weibull plotting position) and the Beta quantile function is pp_r(F) = IIB(F, r, n+1-r), where F represents the nonexceedance probability of the plotting position. IIB is the “inverse of the incomplete beta function” or the quantile function of the Beta distribution as provided in R by `qbeta(f, a, b)`. If F=0.5, then the median is returned but that is conveniently implemented in `pp.median`. Readers might consult Gilchrist (2011, chapter 12) and Karian and Dudewicz (2011, p. 510).

## Usage

 `1` ```pp.f(f, x) ```

## Arguments

 `f` A nonexceedance probability. `x` A vector of data. The ranks and the length of the vector are computed within the function.

## Value

An R `vector` is returned.

## Note

The function uses the R function `rank`, which has specific settings to handle tied data. For implementation here, the `ties.method="first"` method to `rank` is used.

W.H. Asquith

## References

Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.

Karian, Z.A., and Dudewicz, E.J., 2011, Handbook of fitting statistical distributions with R: Boca Raton, FL, CRC Press.

`pp`, `pp.median`

## Examples

 ```1 2 3 4 5``` ```X <- sort(rexp(10)) PPlo <- pp.f(0.25, X) PPhi <- pp.f(0.75, X) plot(c(PPlo,NA,PPhi), c(X,NA,X)) points(pp(X), X) # Weibull i/(n+1) ```

### Example output

```
```

lmomco documentation built on March 14, 2020, 5:06 p.m.