[R] CDFs

[David Winsemius]

On Aug 22, 2011, at 3:50 PM, R. Michael Weylandt wrote:

> Yes. The xCDF/yCDF objects that are returned by the ecdf function  
> can be
> called like functions.

Because they _are_ functions.

 > "function" %in% class(xCDF)
[1] TRUE
 > is.function(xCDF)
[1] TRUE

>
> For example:
>
> x = rnrom(50); xCDF = ecdf(x); xCDF(0.3)
> # This value tells you what fraction of x is less than 0.3
>
> You can also assign this behavior to a function:
>
> F <- function(z) { xCDF(z) }
>
> F does not inherit xCDF directly though and looses the step-function- 
> ness of
> the xCDF object. (Compare plots of F and xCDF to see one consequence)

Not correct. Steps are still there in the same locations.

>
> So yes, you can do subtraction on this basis
>
> x = rnrom(50); Fx = ecdf(x); Fx <- function(z) { xCDF(z) }

You are adding an unnecessary function "layer". Try (after correcting  
the misspelling):

xCDF(seq(-2,2,by=0.02)) == Fx(seq(-2,2,by=0.02)) # => creating Fx is  
superfluous

x <- function(x){function(x) x}  <==> x <- function(x){ x}

"Turtles all the way down."


> y = rnrom(50); yCDF = ecdf(x); Fy <- function(z) { yCDF(z) }
>
> F <- function(z) {Fx(z) - Fy(z)}
> # F <- function(z) {xCDF(z)-yCDF(z)} # Another way to do the same  
> thing

As this would have this:

  F = function(z) xCDF(z)-yCDF(z)
  plot(seq(-2,2,by=0.02), F(seq(-2,2,by=0.02)) ,type="l")

Interesting plot by the way. Unit steps at Gaussian random intervals.  
I'm not sure my intuition would have gotten there all on its own. I  
guess that arises from the discreteness of the sampling. I wasn't  
think that ecdf was the inverse function but seem to remember someone  
(some bloke named Weylandt, now that I check)  saying as much earlier  
in the day.

-- 
David.
>
> Hope this helps,
>
> Michael
>
>
> On Mon, Aug 22, 2011 at 3:30 PM, Jim Silverton <jim.silverton at gmail.com 
> >wrote:
>
>> WHat about if you have two cdfs and you want to subtract them? Like  
>> G(x) -
>> H(x)? Can ecdf do this?
>>
>>
>> On Mon, Aug 22, 2011 at 2:24 PM, R. Michael Weylandt <
>> michael.weylandt at gmail.com> wrote:
>>
>>> Number 1 can be done as follows:
>>>
>>> x = rnorm(50); y = rnorm(50)
>>> xCDF = ecdf(x); yCDF = ecdf(y)
>>>
>>> plot(xCDF)
>>> lines(yCDF,col=2)
>>>
>>> For the other ones, you are going to have to be a little more  
>>> specific as
>>> to how you want to do the approximation...but ?density might be a  
>>> place to
>>> start for #4, assuming you meant density of the PDF. If you meant  
>>> CDF, it I
>>> think that's implicit in number 2.
>>>
>>> Michael Weylandt
>>>
>>> On Mon, Aug 22, 2011 at 2:15 PM, Jim Silverton <jim.silverton at gmail.com 
>>> >wrote:
>>>
>>>> Hello all,
>>>>
>>>> I have two columns of numbers. I would like to do the following:
>>>> (1) Plot both cdfs, F1 and F2 on the same graph.
>>>> (2) Find smoothed approximations of F1 and F2 lets call them  
>>>> F1hat and
>>>> F2hat
>>>> (3) Find values for F1hat when we substitue a value of x in it.
>>>> (4) Find the corresponding densities of the cdfs.
>>>> Any ideas?
>>>>
>>>> --
>>>> Thanks,
>>>> Jim.
>>>>
>>>>       [[alternative HTML version deleted]]
>>>>
>>>> ______________________________________________
>>>> R-help at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>
>>>
>>>
>>
>>
>> --
>> Thanks,
>> Jim.
>>
>>
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
West Hartford, CT