ppoints Ordinates for Probability Plotting

Description

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).

Usage

ppoints(n, a = if(n <= 10) 3/8 else 1/2)

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).

The probability points for the continuous sample quantile types 5 to 9 (see quantile) can be obtained by taking a as, respectively, 1/2, 0, 1, 1/3, and 3/8.

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

qqplot, qqnorm.

Examples

ppoints(4) # the same as  ppoints(1:4)
ppoints(10)
ppoints(10, a = 1/2)

## Visualize including the fractions :
require(graphics)
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(!add && 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")