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computing the variance

4 messages · Wang Tian Hua, Romain Francois, Uwe Ligges +1 more

Wang Tian Hua
# 
hi,
when i was computing the variance of a simple vector, i found unexpect 
result. not sure whether it is a bug.
 > var(c(1,2,3))
[1] 1  #which should be 2/3.
 > var(c(1,2,3,4,5))
[1] 2.5 #which should be 10/5=2

it seems to me that the program uses (sample size -1) instead of sample 
size at the denominator. how can i rectify this?

regards,
tianhua
Romain Francois
# 
Le 05.12.2005 09:53, Wang Tian Hua a ??crit :
These results are expected, it is so not a bug.
 From details section in ?var
    The denominator n - 1 is used which gives an unbiased estimator of
     the (co)variance for i.i.d. observations. (.....)

If you really want biased variance, work around :

biasedVar <- function(x, ...){
  n <- length(x)
  (n-1) / n * var(x,...)
}

Romain
Uwe Ligges
#
Wang Tian Hua wrote:

            

      
      
      
    

        
Not a bug! ?var:
"The denominator n - 1 is used which gives an unbiased estimator of the 
(co)variance for i.i.d. observations."

            

      
      
      
    

        
Simply change it by:

x <- c(1,2,3,4,5)
n <- length(x)
var(x)*(n-1)/n

if you really want it.


Uwe Ligges

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Kristel Joossens
    

    

      
      #
    

  


  

      
Just redefine the var(x) as sum((x-mean(x))^2)/length(x)?
Or straightforward just use var(x)*(1-1/length(x))

As you already mentioned var(x) is now defined by 
sum((x-mean(x))^2)/(length(x)-1) which is an *unbaised* estimtor of COV.
While sum((x-mean(x))^2)/length(x) is a *biased* estimator with
Bias = -1/N COV

Denote population mean by  M
Proof: E[sum (Xj-mean(X))^2] = E[sum Xj^2 - n mean(X)^2]
                       = sum E[Xj^2] - n E[mean(X)^2]
                       = sum (COV + M^2) - n (1/n COV + M^2)
                       = (n-1) COV

Best regards,
Kristel

        
Wang Tian Hua wrote: