Re: [R] A vector of normal distributed values with a sum-to-zero constraint
On 01 Apr 2014, at 17:22 , Rui Barradas wrote: > Hello, > > One way is to use ?scale. > ...except that the sd will be less than 0.5 (not obvious at n=1e6, though). However, if you want - normal distribution - symmetry - constant marginal variance of sigma^2 - fixed sum = 0 I don't see any way more straightforward than generating n normal variates and subtracting the mean. The only snag is that the variance of a residual is sigma^2(1-1/n), so generate the original data with a variance of sigma^2/(1-1/n) = n/(n-1) sigma^2 I.e. x <- rnorm(n,0,0.5*sqrt(n/(n-1))) x <- x - mean(x) All of this applies within the boundaries of numerical precision. You're not going to beat the FPU: > n <- 1e6 > x <- rnorm(n,0,0.5*sqrt(n/(n-1))) > x <- x - mean(x) > sum(x) [1] -1.625718e-11 > mean(x) [1] -1.452682e-17 The problem of getting a sum or mean of _exactly_ 0 is just not well-defined, since sums and averages depend on the summation order: > sum(x) [1] -1.625718e-11 > sum(sample(x)) [1] -1.624851e-11 > sum(sort(x)) [1] -1.508771e-11 > sum(rev(sort(x))) [1] -1.599831e-11 > set.seed(4867) > l <- 100 > aux <- rnorm(l, 0, 0.5) > aux <- scale(aux, scale = FALSE) > sum(aux) > > hist(aux, prob = TRUE) > curve(dnorm(x, 0, 0.5), from = -2, to = 2, add = TRUE) > > Hope this helps, > > Rui Barradas > > Em 01-04-2014 16:01, jlu...@ria.buffalo.edu escreveu: >> Then what's wrong with centering your initial values around the mean? >> >> >> >> Marc Marí Dell'Olmo >> 04/01/2014 10:56 AM >> >> To >> Boris Steipe , >> cc >> jlu...@ria.buffalo.edu, "r-help@r-project.org" >> Subject >> Re: [R] A vector of normal distributed values with a sum-to-zero >> constraint >> >> >> >> >> >> >> Boris is right. I need this vector to include as initial values of a >> MCMC process (with openbugs) and If I use this last approach sum(x) >> could be a large (or extreme) value and can cause problems. >> >> The other approach x <- c(x, -x) has the problem that only vectors >> with even values are obtained. >> >> Thank you! >> >> >> 2014-04-01 16:25 GMT+02:00 Boris Steipe : >>> But the result is not Normal. Consider: >>> >>> set.seed(112358) >>> N <- 100 >>> x <- rnorm(N-1) >>> sum(x) >>> >>> [1] 1.759446 !!! >>> >>> i.e. you have an outlier at 1.7 sigma, and for larger N... >>> >>> set.seed(112358) >>> N <- 1 >>> x <- rnorm(N-1) >>> sum(x) >>> [1] -91.19731 >>> >>> B. >>> >>> >>> On 2014-04-01, at 10:14 AM, jlu...@ria.buffalo.edu wrote: >>> >>>> The sum-to-zero constraint imposes a loss of one degree of freedom. Of >> N samples, only (N-1) can be random. Thus the solution is >>>>> N <- 100 >>>>> x <- rnorm(N-1) >>>>> x <- c(x, -sum(x)) >>>>> sum(x) >>>> [1] -7.199102e-17 >>>> >>>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> >>>> Boris Steipe >>>> Sent by: r-help-boun...@r-project.org >>>> 04/01/2014 09:29 AM >>>> >>>> To >>>> Marc Marí Dell'Olmo , >>>> cc >>>> "r-help@r-project.org" >>>> Subject >>>> Re: [R] A vector of normal distributed values with a sum-to-zero >> constraint >>>> >>>> >>>> >>>> >>>> >>>> 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 Marí 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 <- 100 >>>>>> aux <- rnorm(l,0,0.5) >>>&
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
Hi Marc
I think that we could help you better if we knew in which context you need
sample from a sum constrained normal distribution. However this is more a
question on probability theory than on how to do it in R.
The proposal so far has been linear transformation of multivariate normal
distribution (Marc, Rui), mixture of normal and reflected normal distribution
(Boris, try that with e.g. mu = 2), normal distribution mixed with single point
with positive mass (Jlucke), degenerated normal distribution (Greg).
What you in fact want to do is to draw samples from a conditional distribution.
The condition is the sum constraint so if we have x = (x1, x2, ..., xn) then
sum_{i=1}^n xi = 0 or x1 + x2 + ... x{n-1} = xn so you want to draw samples
from P(x given that x is normal distributed and sum(x)=0). The sum constraint
gives in fact what is called distributions on the simplex. Google for "normal
distribution simplex" and you will get almost 2 mill hits. The second shows how
to sample using Gibbs sampling
(http://dobigeon.perso.enseeiht.fr/papers/Dobigeon_TechReport_2007b.pdf).
However you can probably just use other distributions given sum constraint
since you say that you only need the sample as initial values for a MCMC
algorithm. Many methods are available from "compositional statistics" (google
for that, Aitchison 1986 is the pioneer).
At least two packages are available for R:"compositions" with the latest
version from 2013 and can be found in the archives and "robComposition" still
maintained.
Hope that helps, it is help for yourself to find a solution.
Yours sincerely / Med venlig hilsen
Frede Aakmann Tøgersen
Specialist, M.Sc., Ph.D.
Plant Performance & Modeling
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> -Original Message-
> From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org]
> On Behalf Of Marc Marí Dell'Olmo
> Sent: 1. april 2014 16:57
> To: Boris Steipe
> Cc: r-help@r-project.org
> Subject: Re: [R] A vector of normal distributed values with a sum-to-zero
> constraint
>
> Boris is right. I need this vector to include as initial values of a
> MCMC process (with openbugs) and If I use this last approach sum(x)
> could be a large (or extreme) value and can cause problems.
>
> The other approach x <- c(x, -x) has the problem that only vectors
> with even values are obtained.
>
> Thank you!
>
>
> 2014-04-01 16:25 GMT+02:00 Boris Steipe :
> > But the result is not Normal. Consider:
> >
> > set.seed(112358)
> > N <- 100
> > x <- rnorm(N-1)
> > sum(x)
> >
> > [1] 1.759446 !!!
> >
> > i.e. you have an outlier at 1.7 sigma, and for larger N...
> >
> > set.seed(112358)
> > N <- 1
> > x <- rnorm(N-1)
> > sum(x)
> > [1] -91.19731
> >
> > B.
> >
> >
> > On 2014-04-01, at 10:14 AM, jlu...@ria.buffalo.edu wrote:
> >
> >> The sum-to-zero constraint imposes a loss of one degree of freedom. Of
> N samples, only (N-1) can be random. Thus the solution is
> >> > N <- 100
> >> > x <- rnorm(N-1)
> >> > x <- c(x, -sum(x))
> >> > sum(x)
> >> [1] -7.199102e-17
> >>
> >> >
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >> Boris Steipe
> >> Sent by: r-help-boun...@r-project.org
> >> 04/01/2014 09:29 AM
> >>
> >> To
> >> Marc Marí Dell'Olmo ,
> >> cc
> >> "r-help@r-project.org"
> >> Subject
> >> Re: [R] A vector of normal distributed values with a sum-to-zero
> constraint
> >>
> >>
> >>
> >>
> >>
> >> 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 Marí 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.
> >> >
> >>
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
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 Marí 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 <- 100 >> aux <- rnorm(l,0,0.5) >> s <- sum(aux)/l >> aux2 <- aux-s >> sum(aux2) > [1] -0.0006131392 >> >> aux[1]<- -sum(aux[2:l]) >> sum(aux) > [1] -0.03530422 > > > 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@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. 538...@gmail.com __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
Hello, One way is to use ?scale. set.seed(4867) l <- 100 aux <- rnorm(l, 0, 0.5) aux <- scale(aux, scale = FALSE) sum(aux) hist(aux, prob = TRUE) curve(dnorm(x, 0, 0.5), from = -2, to = 2, add = TRUE) Hope this helps, Rui Barradas Em 01-04-2014 16:01, jlu...@ria.buffalo.edu escreveu: Then what's wrong with centering your initial values around the mean? Marc Marí Dell'Olmo 04/01/2014 10:56 AM To Boris Steipe , cc jlu...@ria.buffalo.edu, "r-help@r-project.org" Subject Re: [R] A vector of normal distributed values with a sum-to-zero constraint Boris is right. I need this vector to include as initial values of a MCMC process (with openbugs) and If I use this last approach sum(x) could be a large (or extreme) value and can cause problems. The other approach x <- c(x, -x) has the problem that only vectors with even values are obtained. Thank you! 2014-04-01 16:25 GMT+02:00 Boris Steipe : But the result is not Normal. Consider: set.seed(112358) N <- 100 x <- rnorm(N-1) sum(x) [1] 1.759446 !!! i.e. you have an outlier at 1.7 sigma, and for larger N... set.seed(112358) N <- 1 x <- rnorm(N-1) sum(x) [1] -91.19731 B. On 2014-04-01, at 10:14 AM, jlu...@ria.buffalo.edu wrote: The sum-to-zero constraint imposes a loss of one degree of freedom. Of N samples, only (N-1) can be random. Thus the solution is N <- 100 x <- rnorm(N-1) x <- c(x, -sum(x)) sum(x) [1] -7.199102e-17 Boris Steipe Sent by: r-help-boun...@r-project.org 04/01/2014 09:29 AM To Marc Marí Dell'Olmo , cc "r-help@r-project.org" Subject Re: [R] A vector of normal distributed values with a sum-to-zero constraint 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 Marí 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 <- 100 aux <- rnorm(l,0,0.5) s <- sum(aux)/l aux2 <- aux-s sum(aux2) [1] -0.0006131392 aux[1]<- -sum(aux[2:l]) sum(aux) [1] -0.03530422 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@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. __ R-help@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. __ R-help@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. [[alternative HTML version deleted]] __ R-help@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. __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
Then what's wrong with centering your initial values around the mean? Marc Marí Dell'Olmo 04/01/2014 10:56 AM To Boris Steipe , cc jlu...@ria.buffalo.edu, "r-help@r-project.org" Subject Re: [R] A vector of normal distributed values with a sum-to-zero constraint Boris is right. I need this vector to include as initial values of a MCMC process (with openbugs) and If I use this last approach sum(x) could be a large (or extreme) value and can cause problems. The other approach x <- c(x, -x) has the problem that only vectors with even values are obtained. Thank you! 2014-04-01 16:25 GMT+02:00 Boris Steipe : > But the result is not Normal. Consider: > > set.seed(112358) > N <- 100 > x <- rnorm(N-1) > sum(x) > > [1] 1.759446 !!! > > i.e. you have an outlier at 1.7 sigma, and for larger N... > > set.seed(112358) > N <- 1 > x <- rnorm(N-1) > sum(x) > [1] -91.19731 > > B. > > > On 2014-04-01, at 10:14 AM, jlu...@ria.buffalo.edu wrote: > >> The sum-to-zero constraint imposes a loss of one degree of freedom. Of N samples, only (N-1) can be random. Thus the solution is >> > N <- 100 >> > x <- rnorm(N-1) >> > x <- c(x, -sum(x)) >> > sum(x) >> [1] -7.199102e-17 >> >> > >> >> >> >> >> >> >> >> >> Boris Steipe >> Sent by: r-help-boun...@r-project.org >> 04/01/2014 09:29 AM >> >> To >> Marc Marí Dell'Olmo , >> cc >> "r-help@r-project.org" >> Subject >> Re: [R] A vector of normal distributed values with a sum-to-zero constraint >> >> >> >> >> >> 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 Marí 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 <- 100 >> >> aux <- rnorm(l,0,0.5) >> >> s <- sum(aux)/l >> >> aux2 <- aux-s >> >> sum(aux2) >> > [1] -0.0006131392 >> >> >> >> aux[1]<- -sum(aux[2:l]) >> >> sum(aux) >> > [1] -0.03530422 >> > >> > >> > 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@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. >> >> __ >> R-help@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. >> > > __ > R-help@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. [[alternative HTML version deleted]] __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
It seems so simple to me, that I must be missing something. Subject to Jeff Newmiller's reminder of FAQ 7.31; if the sum is zero then the mean is zero and vice versa. The OP's original attempt of: - l <- 100 aux <- rnorm(l,0,0.5) s <- sum(aux)/l aux2 <- aux-s sum(aux2) - is equivalent to aux2 <- rnorm(l,0,0.5) aux2 <- aux2-mean(aux2) If calculations were exact then aux2 would have mean, and thus sum, equal to zero - any difference from zero is attributable entirely to machine precision. On 01/04/2014 15:25, Boris Steipe wrote: But the result is not Normal. Consider: set.seed(112358) N <- 100 x <- rnorm(N-1) sum(x) [1] 1.759446 !!! i.e. you have an outlier at 1.7 sigma, and for larger N... set.seed(112358) N <- 1 x <- rnorm(N-1) sum(x) [1] -91.19731 B. On 2014-04-01, at 10:14 AM, jlu...@ria.buffalo.edu wrote: The sum-to-zero constraint imposes a loss of one degree of freedom. Of N samples, only (N-1) can be random. Thus the solution is N <- 100 x <- rnorm(N-1) x <- c(x, -sum(x)) sum(x) [1] -7.199102e-17 Boris Steipe Sent by: r-help-boun...@r-project.org 04/01/2014 09:29 AM To Marc Marí Dell'Olmo , cc "r-help@r-project.org" Subject Re: [R] A vector of normal distributed values with a sum-to-zero constraint 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 Marí 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 <- 100 aux <- rnorm(l,0,0.5) s <- sum(aux)/l aux2 <- aux-s sum(aux2) [1] -0.0006131392 aux[1]<- -sum(aux[2:l]) sum(aux) [1] -0.03530422 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@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. __ R-help@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. __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
Boris is right. I need this vector to include as initial values of a MCMC process (with openbugs) and If I use this last approach sum(x) could be a large (or extreme) value and can cause problems. The other approach x <- c(x, -x) has the problem that only vectors with even values are obtained. Thank you! 2014-04-01 16:25 GMT+02:00 Boris Steipe : > But the result is not Normal. Consider: > > set.seed(112358) > N <- 100 > x <- rnorm(N-1) > sum(x) > > [1] 1.759446 !!! > > i.e. you have an outlier at 1.7 sigma, and for larger N... > > set.seed(112358) > N <- 1 > x <- rnorm(N-1) > sum(x) > [1] -91.19731 > > B. > > > On 2014-04-01, at 10:14 AM, jlu...@ria.buffalo.edu wrote: > >> The sum-to-zero constraint imposes a loss of one degree of freedom. Of N >> samples, only (N-1) can be random. Thus the solution is >> > N <- 100 >> > x <- rnorm(N-1) >> > x <- c(x, -sum(x)) >> > sum(x) >> [1] -7.199102e-17 >> >> > >> >> >> >> >> >> >> >> >> Boris Steipe >> Sent by: r-help-boun...@r-project.org >> 04/01/2014 09:29 AM >> >> To >> Marc Marí Dell'Olmo , >> cc >> "r-help@r-project.org" >> Subject >> Re: [R] A vector of normal distributed values with a sum-to-zero >> constraint >> >> >> >> >> >> 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 Marí 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 <- 100 >> >> aux <- rnorm(l,0,0.5) >> >> s <- sum(aux)/l >> >> aux2 <- aux-s >> >> sum(aux2) >> > [1] -0.0006131392 >> >> >> >> aux[1]<- -sum(aux[2:l]) >> >> sum(aux) >> > [1] -0.03530422 >> > >> > >> > 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@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. >> >> __ >> R-help@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. >> > > __ > R-help@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. __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
But the result is not Normal. Consider: set.seed(112358) N <- 100 x <- rnorm(N-1) sum(x) [1] 1.759446 !!! i.e. you have an outlier at 1.7 sigma, and for larger N... set.seed(112358) N <- 1 x <- rnorm(N-1) sum(x) [1] -91.19731 B. On 2014-04-01, at 10:14 AM, jlu...@ria.buffalo.edu wrote: > The sum-to-zero constraint imposes a loss of one degree of freedom. Of N > samples, only (N-1) can be random. Thus the solution is > > N <- 100 > > x <- rnorm(N-1) > > x <- c(x, -sum(x)) > > sum(x) > [1] -7.199102e-17 > > > > > > > > > > > > Boris Steipe > Sent by: r-help-boun...@r-project.org > 04/01/2014 09:29 AM > > To > Marc Marí Dell'Olmo , > cc > "r-help@r-project.org" > Subject > Re: [R] A vector of normal distributed values with a sum-to-zero > constraint > > > > > > 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 Marí 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 <- 100 > >> aux <- rnorm(l,0,0.5) > >> s <- sum(aux)/l > >> aux2 <- aux-s > >> sum(aux2) > > [1] -0.0006131392 > >> > >> aux[1]<- -sum(aux[2:l]) > >> sum(aux) > > [1] -0.03530422 > > > > > > 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@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. > > __ > R-help@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. > __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
The sum-to-zero constraint imposes a loss of one degree of freedom. Of N samples, only (N-1) can be random. Thus the solution is > N <- 100 > x <- rnorm(N-1) > x <- c(x, -sum(x)) > sum(x) [1] -7.199102e-17 > Boris Steipe Sent by: r-help-boun...@r-project.org 04/01/2014 09:29 AM To Marc Marí Dell'Olmo , cc "r-help@r-project.org" Subject Re: [R] A vector of normal distributed values with a sum-to-zero constraint 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 Marí 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 <- 100 >> aux <- rnorm(l,0,0.5) >> s <- sum(aux)/l >> aux2 <- aux-s >> sum(aux2) > [1] -0.0006131392 >> >> aux[1]<- -sum(aux[2:l]) >> sum(aux) > [1] -0.03530422 > > > 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@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. __ R-help@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. [[alternative HTML version deleted]] __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
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 Marí 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 <- 100 >> aux <- rnorm(l,0,0.5) >> s <- sum(aux)/l >> aux2 <- aux-s >> sum(aux2) > [1] -0.0006131392 >> >> aux[1]<- -sum(aux[2:l]) >> sum(aux) > [1] -0.03530422 > > > 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@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. __ R-help@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.
Re: [R] A vector of normal distributed values with a sum-to-zero constraint
You are on a fool's errand. Read FAQ 7.31. --- Jeff NewmillerThe . . Go Live... DCN:Basics: ##.#. ##.#. Live Go... Live: OO#.. Dead: OO#.. Playing Research Engineer (Solar/BatteriesO.O#. #.O#. with /Software/Embedded Controllers) .OO#. .OO#. rocks...1k --- Sent from my phone. Please excuse my brevity. On April 1, 2014 5:56:24 AM PDT, "Marc Marí 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 <- 100 >> aux <- rnorm(l,0,0.5) >> s <- sum(aux)/l >> aux2 <- aux-s >> sum(aux2) >[1] -0.0006131392 >> >> aux[1]<- -sum(aux[2:l]) >> sum(aux) >[1] -0.03530422 > > >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@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. __ R-help@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.
