[R] probability plot correlation coefficient

[kjetil brinchmann halvorsen]

On 6 Aug 2003 at 19:58, anne wrote:

It is not very clear what you want. For fitting distributions like 
you mentiones, the easiest way for you is maximum likelihood
via fitdistr() in package MASS:

library(MASS)
?fitdistr
x <- rweibull(100, shape=3, scale=2)
fitdistr(x, dweibull, start=list(shape=5, scale=0.5) )
     shape       scale  
  3.1391369   2.0803995 
 (0.2383695) (0.0700139)


I don't know about PPCC, but it looks like you want to estimate the 
shape by selecting the shape to maximize the correlation coefficient 
in a probability plot. While that makes intuitive sense, what I have 
given above is probably better. 

If you want to get the correlation coefficient corresponding to a 
probability plot, it is easy:

 qqplot( qweibull(ppoints(x), shape=3, scale=2), x )
cor( qweibull(ppoints(x), shape=3, scale=2), sort(x) )
[1] 0.9940447

and you can even easily write a function to do PPCC (If i have 
understood it correctly): (But the example also show that if I have 
understood correctly, it is'nt a very good or reliable method)

> PPCC <- function(shape, scale, x) { # only for weibull
+           x <- sort(x)
+           pp <- ppoints(x)
+           cor( qweibull(pp, shape=shape, scale=scale), x)}
> PPCC(3,2,x)
[1] 0.9940447

> optim(par=c(shape=5, scale=0.5), function(par) PPCC(par[1], par[2],x), 
+                 method="BFGS")
$par
  shape   scale 
99.9199  0.5000 

$value
[1] 0.9490552

$counts
function gradient 
      12       11 

$convergence
[1] 0

$message
NULL

> optim(par=c(shape=5, scale=2), function(par) PPCC(par[1], par[2],x), 
+                 method="BFGS")
$par
  shape   scale 
99.9199  2.0000 

$value
[1] 0.9490552

$counts
function gradient 
      12       11 

$convergence
[1] 0

$message
NULL

> optim(par=c(shape=3, scale=2), function(par) PPCC(par[1], par[2],x), 
+                 method="BFGS")
$par
   shape    scale 
3.403016 2.000000 

$value
[1] 0.992391

$counts
function gradient 
     100      100 

$convergence
[1] 1

$message
NULL


As the example show, you need some very good starting value to get 
something reasonable. Strick with fitdistr()!

Kjetil Halvorsen



> As a newbie to R, I'm still rather at a loss for finding information 
> (the commands names can be rather arcane)so I'm just posting my question:
> I would like to estimate   the shape coefficient of diverse 
> distributions (Weibull, gamma and Tukey-Lambda specifically, but other 
> could be of interest)
> - Does R have a PPCC utility to estimate such parameter?(maximum value 
> of correlation coef)
> - If yes how does one retrieve the numerical value from the graph? (see 
> graphical example below)
> - The retrieval of numerical values is also a problem for me from the 
> probability plots....
> 
> 
> 
> 
> Thank for any help!
> Anne
> 
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