[R] Confidence Bounds on QQ Plots?

Uwe Ligges ligges at statistik.uni-dortmund.de
Tue Jun 1 22:03:46 CEST 2004

Spencer Graves wrote:
>      What's the current best wisdom on how to construct confidence 
> bounds on something like a normal probability plot?
>      I recall having read a suggestion to Monte Carlo something like 201 
> simulated lines with the same number of points, then sort the order 
> statistics, and plot the 6th and 196th of these.  [I use 201 not 200 
> because quantile(1:201, c(0.025, 0.975)) = 6 and 196 while 
> quantile(1:200, c(0.025, 0.975)) = 5.975 and 11.025.]  I think I know 
> how to do this, but before I code it, I'd like to ask two questions on 
> this issue:
>      1.  Where can I find this in the literature?  I didn't find it 
> where I thought it was, nor in anyplace else that seemed obvious to me, 
> but I don't think I made it up and I'd like to give credit where credit 
> it due.
>      2.  Are there better alternatives available, especially if the 
> distribution is a compound mixture that is easily simulated but not so 
> easily characterized analytically?
>      Thanks,
>      spencer graves
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John Fox has qq.plot() in his "car" package for (not only) plotting 
pointwise confidence envelops into QQ-Plots.

See his books:

  author =       "Fox,~J.",
  title=         {{Applied Regression Analysis, Linear Models, and 
Related Methods}},
  publisher =    {Sage},
  address =      "Thousand Oaks",
  year =         "1997"
  author =       "Fox,~J.",
  title=         {{An R and S-PLUS Companion to Applied Regression}},
  publisher =    {Sage},
  address =      "Thousand Oaks",
  year =         "2002"

Uwe Ligges

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