cumulative kurtosis

[spsanderson]

Function:

#' Cumulative Kurtosis
#' 
#' @family Vector Function
#' 
#' @author Steven P. Sanderson II, MPH
#' 
#' @details
#' A function to return the cumulative kurtosis of a vector.
#' 
#' @description 
#' A function to return the cumulative kurtosis of a vector.
#' 
#' @parm .x A numeric vector
#' 
#' @examples 
#' x <- mtcars$mpg
#' 
#' ckurtosis(x)
#' 
#' @return 
#' A numeric vector
#' 
#' @export
#' 

ckurtosis <- function(.x){
  kurtosis <- function(.x){
    length(.x) * sum((.x - mean(.x))^4) / (sum((.x - mean(.x))^2)^2)
  }
  sapply(seq_along(.x), function(k, z) kurtosis(z[1:k]), z = .x)
}

Example:

x <- mtcars$mpg

> ckurtosis(x)
 [1]      NaN      NaN 1.500000 2.189216 2.518932 1.786006 2.744467 2.724675
 [9] 2.930885 2.988093 2.690270 2.269038 2.176622 1.992044 2.839430 2.481896
[17] 2.356826 3.877115 3.174702 2.896931 3.000743 3.091225 3.182071 3.212816
[25] 3.352916 3.015952 2.837139 2.535185 2.595908 2.691103 2.738468 2.799467