[R] Sharp turn in cdf?

[David Winsemius]

On Aug 26, 2011, at 9:12 AM, David Winsemius wrote:

> This arrived without a refers to in its headers and was a follow up  
> to:
>
> On Aug 25, 2011, at 9:33 PM, Jim Silverton wrote:
>>> Hi all,
>>> I have some data. I want to fit a smooth cdf to the data. Then I  
>>> want to
>>> find both the value of x  and the % on the y axis for which the  
>>> the slope is
>>> 1 ( or the point where the slope change is the greatest...hummh  
>>> well the
>>> part where you can identify where there is a point of  
>>> inflection...for want
>>> of a better word. Any ideas?
> On Aug 26, 2011, at 12:59 AM, Jim Silverton wrote:
>
>> x = c(runif(1000, 0,2.5), runif(100, 2.5, 4))
>> plot(ecdf(x))
>>
>> You will notice a sharp turn around x = 2.5
>> How do I get that value of x using R?
>
> So you are not interested in a specific slope or in the inflection  
> points (since there is no no inflection in this example but rather  
> in the point at which the slope changes. The is a package,  
> structcahange  that looks at segmented models but in this simple  
> instance I could not get it to return resuslts that I thought were  
> consistent with the data.

Not one of my better speling efforts. The package name is 'strucchange'

http://finzi.psych.upenn.edu/R/library/strucchange/doc/strucchange-intro.pdf

These were my half-assed efforts that did not produce what seemed to  
be an accurate estimate, but I'm not a user of htat package and maybe  
someone can throw me a clue sincse that example seemed so "easy".

library(strucchange)

# After reading (skimming actually) the vignette and the help page for  
Fstats
 > fs.x <- Fstats(x ~ 1)
 > plot(fs.x)
 > breakpoints(fs.x)

	 Optimal 2-segment partition:

Call:
breakpoints.Fstats(obj = fs.x)

Breakpoints at observation number:
935

Corresponding to breakdates:
0.8490909

>
> In a sense it is like a statistical process control problem. Cusums  
> are often used to follow measurements that have a random and  
> systematic component and which may shift their behavior. This is a  
> simple demonstration of the advantages of that approach. Just take  
> the median value and track cumulative sums:
>
> csum.x <- cumsum(x-median(x))
> plot( csum.x)
> which.min(csum.x)
> #'[1] 999
>
> -- 
> David Winsemius, MD
> West Hartford, CT
>
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David Winsemius, MD
West Hartford, CT