How to find the statistical mode?

Question

In R, mean() and median() are standard functions which do what you\'d expect. mode() tells you the internal storage mode of the objec

Answer 1

It seems to me that if a collection has a mode, then its elements can be mapped one-to-one with the natural numbers. So, the problem of finding the mode reduces to producing such a mapping, finding the mode of the mapped values, then mapping back to some of the items in the collection. (Dealing with NA occurs at the mapping phase).

I have a histogram function that operates on a similar principal. (The special functions and operators used in the code presented herein should be defined in Shapiro and/or the neatOveRse. The portions of Shapiro and neatOveRse duplicated herein are so duplicated with permission; the duplicated snippets may be used under the terms of this site.) R pseudocode for histogram is

.histogram <- function (i)
        if (i %|% is.empty) integer() else
        vapply2(i %|% max %|% seqN, `==` %<=% i %O% sum)

histogram <- function(i) i %|% rmna %|% .histogram

(The special binary operators accomplish piping, currying, and composition) I also have a maxloc function, which is similar to which.max, but returns all the absolute maxima of a vector. R pseudocode for maxloc is

FUNloc <- function (FUN, x, na.rm=F)
        which(x == list(identity, rmna)[[na.rm %|% index.b]](x) %|% FUN)

maxloc <- FUNloc %<=% max

minloc <- FUNloc %<=% min # I'M THROWING IN minloc TO EXPLAIN WHY I MADE FUNloc

Then

imode <- histogram %O% maxloc

and

x %|% map %|% imode %|% unmap

will compute the mode of any collection, provided appropriate map-ping and unmap-ping functions are defined.