[R] question about extreme value distribution

[Greg Snow]

As an alternative you could try quantile regression (find a regression
line for the 95th percentile), if the relationship between max(y) and x
is only due to more points (and therefore more oportunities for large
values) then the estimated quantile lines should not differ
significantly from 0.

Try the following (where the truth is no relationship):

set.seed(2)

x <- rep(1:10, 1:10)
y <- rexp(55, 1)

plot(x,y)

cor.test( 1:10, tapply( y, x, max ) )

library(quantreg)
fit <- rq( y ~ x, tau=c(0.5, 0.95) )
summary(fit)


Notice that the cor.test is significant, but that the confidence
intervals for the slopes both include 0.

Hope this helps,

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at intermountainmail.org
(801) 408-8111
 
 

> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Avril Coghlan
> Sent: Thursday, November 22, 2007 5:46 AM
> To: r-help at stat.math.ethz.ch
> Cc: alc at sanger.ac.uk
> Subject: [R] question about extreme value distribution
> 
> Hello,
> 
> I have a question about using extreme
> value distribution in R. 
> 
> I have two variables, X and Y, and have pairs of points 
> (X1,Y1),(X2,Y2), (X3,Y3) etc.
> When I plot X against Y, it looks
> like the maximum value of Y (for a particular X) is correlated with X.
> 
> Indeed, when I bin the data by X-value into equally sized 
> bins, and test whether the maximum value of Y for a bin is 
> correlated with the mean X for the bin, there is a 
> significant correlation between max(Y) and X. However, I am 
> not very happy with this because there is not an equal number 
> of data points in each bin.
> 
> I imagine that there is a better statistical test that I 
> could use, if I could fit an extreme value distribution to the Y data.
> However, I'm not sure how to do this. 
> I am wondering is there a way to use the extreme value 
> distribution functions in R to test the hypothesis that the 
> maximum of Y (for a particular X) is correlated with X?
> 
> I would appreciate advice very much.
> 
> regards
> Avril Coghlan
> 
> 
> 
> 
> 
> 
> 
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