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).

distribution, arith, dplot
ppoints(n, a = if(n 
either the number of points generated or a vector of observations.
the offset fraction to be used; typically in $(0,1)$.

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).


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.

  • ppoints
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

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