How to scale/transform graphics::plot() axes with any transformation, not just logarithmic (for Weibull plots)?

I am building an R package to display Weibull plots (using graphics::plot) in R. The plot has a log-transformed x-axis and a Weibull-transformed y-axis (for lack of a better description). The two-parameter Weibull distribution can thus be represented as a straight line on this plot.

The logarithmic transformation of the x-axis is as simple as adding the log="x" parameter to plot() or curve(). How can I supply the y-axis transformation in an elegant way, so that all graphics-related plotting will work on my axis-transformed plot? To demonstrate what I need, run the following example code:

## initialisation ##
beta     <- 2;eta <- 1000
ticks    <- c(seq(0.01,0.09,0.01),(1:9)/10,seq(0.91,0.99,0.01))
F0inv    <- function (p) log(qweibull(p, 1, 1))
    # this is the transformation function
F0       <- function (q) exp(-exp(q))
    # this is the inverse of the transformation function
weibull  <- function(x)pweibull(x,beta,eta)
    # the curve of this function represents the weibull distribution 
    # as a straight line on weibull paper
weibull2 <- function(x)F0inv(weibull(x))

First an example of a Weibull distribution with beta=2 and eta=1000 on a regular, untransformed plot:

## untransformed axes ##
curve(weibull ,xlim=c(100,1e4),ylim=c(0.01,0.99))
abline(h=ticks,col="lightgray")

This plot is useless for Weibull analysis. Here is my currently implemented solution that transforms the data with function F0inv() and modifies the y-axis of the plot. Notice that I have to use F0inv() on all y-axis related data.

## transformed axis with F0inv() ##
curve(weibull2,xlim=c(100,1e4),ylim=F0inv(c(0.01,0.99)),log="x",axes=F)
axis(1);axis(2,at=F0inv(ticks),labels=ticks)
abline(h=F0inv(ticks),col="lightgray")

This works, but this is not very user-friendly: when the user wants to add annotations, one must always use F0inv():

text(300,F0inv(0.4),"at 40%")

I found that you can achieve a solution to my problem using ggplot2 and scales, but I don't want to change to a graphics package unless absolutely necessary since a lot of other code needs to be rewritten.

## with ggplot2 and scales ##
library(ggplot2)
library(scales)
weibull_trans <- function()trans_new("weibull", F0inv, F0)
qplot(c(100,1e4),xlim=c(100,1e4),ylim=c(0.01,0.99),
    stat="function",geom="line",fun=weibull) + 
    coord_trans(x="log10",y = "weibull")

I think that if I could dynamically replace the code for applying the logarithmic transformation with my own, my problem would be solved.

I tried to find more information by Googling "R axis transformation", "R user coordinates", "R axis scaling" without useful results. Almost everything I have found dealt with logarithmic scales.

I tried to look into plot() at how the log="x" parameter works, but the relevant code for plot.window is written in C – not my strongest point at all.

While it doesn't appear to be possible in base graphics, you can make this function do what you want so that you can call it more simply:

F0inv    <- function (p) log(qweibull(p, 1, 1))
## this is the transformation function
F0       <- function (q) exp(-exp(q))

weibullplot <- function(eta, beta,
                        ticks=c(seq(0.01,0.09,0.01),(1:9)/10,seq(0.91,0.99,0.01)),
                        ...) {
  ## the curve of this function represents the weibull distribution 
  ## as a straight line on weibull paper
  weibull2 <- function(x)
    F0inv(pweibull(x, beta, eta))
  curve(weibull2, xlim=c(100, 1e4), ylim=F0inv(c(0.01, 0.99)), log="x", axes=FALSE)
  axis(1);
  axis(2, at=F0inv(ticks), labels=ticks)
  abline(h=F0inv(ticks),col="lightgray")
}

weibullplot(eta=1000, beta=2)

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