# ppoints

##### Ordinates for Probability Plotting

Generates the sequence of probability points
`(1:m - a)/(m + (1-a)-a)`

where `m`

is either `n`

, if `length(n)==1`

, or
`length(n)`

.

- Keywords
- distribution, arith, dplot

##### Usage

`ppoints(n, a = if(n `

##### Arguments

- n
- either the number of points generated or a vector of observations.
- a
- the offset fraction to be used; typically in $(0,1)$.

##### Details

If $0 < a < 1$, the resulting values are within $(0,1)$
(excluding boundaries).
In any case, the resulting sequence is symmetric in $[0,1]$, i.e.,
`p + rev(p) == 1`

.

`ppoints()`

is used in `qqplot`

and `qqnorm`

to generate
the set of probabilities at which to evaluate the inverse distribution.

The choice of `a`

follows the documentation of the function of the
same name in Becker *et al* (1988), and appears to have been
motivated by results from Blom (1958) on approximations to expect normal
order statistics (see also `quantile`

).

##### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
*The New S Language*.
Wadsworth & Brooks/Cole.

Blom, G. (1958)
*Statistical Estimates and Transformed Beta Variables.*
Wiley

##### See Also

##### Examples

`library(stats)`

```
ppoints(4) # the same as ppoints(1:4)
ppoints(10)
ppoints(10, a = 1/2)
## Visualize including the fractions :
require(graphics)lNs <- loadedNamespaces()
p.ppoints <- function(n, ..., add = FALSE, col = par("col")) {
pn <- ppoints(n, ...)
if(add)
points(pn, pn, col=col)
else {
tit <- match.call(); tit[[1]] <- quote(ppoints)
plot(pn,pn, main = deparse(tit), col=col,
xlim=0:1, ylim=0:1, xaxs="i", yaxs="i")
abline(0,1, col = adjustcolor(1, 1/4), lty = 3)
}
if(requireNamespace("MASS", quietly=TRUE))
text(pn, pn, as.character(MASS::fractions(pn)),
adj = c(0,0)-1/4, cex = 3/4, xpd = NA, col=col)
abline(h=pn, v=pn, col = adjustcolor(col, 1/2), lty = 2, lwd = 1/2)
}
p.ppoints(4)
p.ppoints(10)
p.ppoints(10, a = 1/2)
p.ppoints(21)
p.ppoints(8) ; p.ppoints(8, a = 1/2, add=TRUE, col="tomato")
if(!any("MASS" == lNs)) unloadNamespace("MASS")
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*