R help - Apr 2014 - A vector of normal distributed values with a sum-to-zero constraint

Dear all,

Anyone knows how to generate a vector of Normal distributed values
(for example N(0,0.5)), but with a sum-to-zero constraint??

The sum would be exactly zero, without decimals.

I made some attempts:
> l <- 1000000
> aux <- rnorm(l,0,0.5)
> s <- sum(aux)/l
> aux2 <- aux-s
> sum(aux2)
[1] -0.000000000006131392
>
> aux[1]<- -sum(aux[2:l])
> sum(aux)
[1] -0.00000000000003530422


but the sum is not exactly zero and not all parameters are N(0,0.5)
distributed...

Perhaps is obvious but I can't find the way to do it..

Thank you very much!

Marc

You are on a fool's errand. Read FAQ 7.31.
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On April 1, 2014 5:56:24 AM PDT, "Marc Mar? Dell'Olmo"
<marceivissa at gmail.com> wrote:
>Dear all,
>
>Anyone knows how to generate a vector of Normal distributed values
>(for example N(0,0.5)), but with a sum-to-zero constraint??
>
>The sum would be exactly zero, without decimals.
>
>I made some attempts:
>
>> l <- 1000000
>> aux <- rnorm(l,0,0.5)
>> s <- sum(aux)/l
>> aux2 <- aux-s
>> sum(aux2)
>[1] -0.000000000006131392
>>
>> aux[1]<- -sum(aux[2:l])
>> sum(aux)
>[1] -0.00000000000003530422
>
>
>but the sum is not exactly zero and not all parameters are N(0,0.5)
>distributed...
>
>Perhaps is obvious but I can't find the way to do it..
>
>Thank you very much!
>
>Marc
>
>______________________________________________
>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.

Make a copy with opposite sign. This is Normal, symmetric, but no longer random.

  set.seed(112358)
  x <- rnorm(5000, 0, 0.5)
  x <- c(x, -x)
  sum(x)
  hist(x)

B.

On 2014-04-01, at 8:56 AM, Marc Mar? Dell'Olmo wrote:
> Dear all,
> 
> Anyone knows how to generate a vector of Normal distributed values
> (for example N(0,0.5)), but with a sum-to-zero constraint??
> 
> The sum would be exactly zero, without decimals.
> 
> I made some attempts:
> 
>> l <- 1000000
>> aux <- rnorm(l,0,0.5)
>> s <- sum(aux)/l
>> aux2 <- aux-s
>> sum(aux2)
> [1] -0.000000000006131392
>> 
>> aux[1]<- -sum(aux[2:l])
>> sum(aux)
> [1] -0.00000000000003530422
> 
> 
> but the sum is not exactly zero and not all parameters are N(0,0.5)
> distributed...
> 
> Perhaps is obvious but I can't find the way to do it..
> 
> Thank you very much!
> 
> Marc
> 
> ______________________________________________
> 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.

Here is one approach to generating a set (or in this case multiple
sets) of normals that sum to 0 (with a little round off error) and
works for an odd number of points:

v <- matrix(-1/8, 9, 9)
diag(v) <- 1
eigen(v)
x <- mvrnorm(100,mu=rep(0,9), Sigma=v, empirical=TRUE)
rowSums(x)
range(.Last.value)
hist(x)
sd(x)
mean(x)
apply(x,2,sd)


the key is to find the value of the off diagonals in the covariance
matrix that gives you exactly one eigenvalue that is equal to 0 (or
close enough with rounding) and all the others are positive.  There is
probably a mathematical formula that gives the exact value to use, but
I found one that works with a little trial and error (it will change
for different sample sizes).

On Tue, Apr 1, 2014 at 6:56 AM, Marc Mar? Dell'Olmo
<marceivissa at gmail.com> wrote:
> Dear all,
>
> Anyone knows how to generate a vector of Normal distributed values
> (for example N(0,0.5)), but with a sum-to-zero constraint??
>
> The sum would be exactly zero, without decimals.
>
> I made some attempts:
>
>> l <- 1000000
>> aux <- rnorm(l,0,0.5)
>> s <- sum(aux)/l
>> aux2 <- aux-s
>> sum(aux2)
> [1] -0.000000000006131392
>>
>> aux[1]<- -sum(aux[2:l])
>> sum(aux)
> [1] -0.00000000000003530422
>
>
> but the sum is not exactly zero and not all parameters are N(0,0.5)
> distributed...
>
> Perhaps is obvious but I can't find the way to do it..
>
> Thank you very much!
>
> Marc
>
> ______________________________________________
> 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.


-- 
Gregory (Greg) L. Snow Ph.D.
538280 at gmail.com