R function for percentrank

David Winsemius <dwinsemius at comcast.net> wrote in 
news:Xns99F989B3A3057dNOTwinscomcast at 80.91.229.13:

"tom soyer" <tom.soyer at gmail.com> wrote in
news:65cc7bdf0712010951p451a993i70da89f285d801de at mail.gmail.com: 

John,

The Excel's percentrank function works like this: if one has a number,
x for example, and one wants to know the percentile of this number in
a given data set, dataset, one would type =percentrank(dataset,x) in
Excel to calculate the percentile. So for example, if the data set is
c(1:10), and one wants to know the percentile of 2.5 in the data set,
then using the percentrank function one would get 0.166, i.e., 2.5 is
in the 16.6th percentile. 

I am not sure how to program this function in R. I couldn't find it as
a built-in function in R either. It seems to be an obvious choice for
a built-in function. I am very surprised, but maybe we both missed it.

 
My nomination for a function with a similar result would be ecdf(), the 
empirical cumulative distribution function. It is of class "function" 

so 

efforts to index ecdf(.)[.] failed for me.

You can use ls.str() to look into the function environment:

ls.str(environment(ecdf(x)))

f :  num 0
method :  int 2
n :  int 25
x :  num [1:25] -2.215 -1.989 -0.836 -0.820 -0.626 ...
y :  num [1:25] 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32 0.36 0.4 ...
yleft :  num 0
yright :  num 1



You can then use get() or mget() within the function environment to
return the requisite values. Something along the lines of the following
within the function percentrank():

percentrank <- function(x, val)
{
  env.x <- environment(ecdf(x))
  res <- mget(c("x", "y"), env.x)
  Ind <- which(sapply(seq(length(res$x)),
                      function(i) isTRUE(all.equal(res$x[i], val))))
  res$y[Ind]
}


Thus:

set.seed(1)
x <- rnorm(25)

x

[1] -0.62645381  0.18364332 -0.83562861  1.59528080  0.32950777
 [6] -0.82046838  0.48742905  0.73832471  0.57578135 -0.30538839
[11]  1.51178117  0.38984324 -0.62124058 -2.21469989  1.12493092
[16] -0.04493361 -0.01619026  0.94383621  0.82122120  0.59390132
[21]  0.91897737  0.78213630  0.07456498 -1.98935170  0.61982575

percentrank(x, 0.48742905)

[1] 0.56


One other approach, which returns the values and their respective rank
percentiles is:

cumsum(prop.table(table(x)))

-2.2146998871775   -1.98935169586337  -0.835628612410047 
               0.04                0.08                0.12 
 -0.820468384118015  -0.626453810742333  -0.621240580541804 
               0.16                0.20                0.24 
 -0.305388387156356 -0.0449336090152308 -0.0161902630989461 
               0.28                0.32                0.36 
 0.0745649833651906   0.183643324222082   0.329507771815361 
               0.40                0.44                0.48 
  0.389843236411431   0.487429052428485   0.575781351653492 
               0.52                0.56                0.60 
  0.593901321217509    0.61982574789471   0.738324705129217 
               0.64                0.68                0.72 
  0.782136300731067   0.821221195098089   0.918977371608218 
               0.76                0.80                0.84 
    0.9438362106853    1.12493091814311    1.51178116845085 
               0.88                0.92                0.96 
   1.59528080213779 
               1.00 

HTH,

Marc Schwartz