# Integer Sample with Mean Dependent on Size

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## Integer Sample with Mean Dependent on Size

 Dear All, I cannot unfortunately provide any R code, otherwise I would not need to post this in the first place. I need to generate a sample of N positive non-zero integers such that their mean is *exactly* 2(N-1)/N, i.e. the mean depends on the length of the sample. For a start, we can assume that every integer in my sample can assume only the values 1, 2 and 3. Any suggestion is appreciated. Cheers Lorenzo ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Integer Sample with Mean Dependent on Size

 n_1 + ... + n_N = 2(N-1) is requested for integers n_i >= 1. What about c(rep(2, N-2), 1, 1))? but I'm afraid that this was not what you really wanted. ;-) However, you didn't say if your sample should be random. :-)   Best regards  --  Gerrit --------------------------------------------------------------------- Dr. Gerrit Eichner                   Mathematical Institute, Room 212 [hidden email]   Justus-Liebig-University Giessen Tel: +49-(0)641-99-32104          Arndtstr. 2, 35392 Giessen, Germany http://www.uni-giessen.de/eichner--------------------------------------------------------------------- Am 01.08.2019 um 12:27 schrieb Lorenzo Isella: > Dear All, > I cannot unfortunately provide any R code, otherwise I would not need to > post this in the first place. > I need to generate a sample of N positive non-zero integers such that > their mean is *exactly* 2(N-1)/N, i.e. the mean depends on the length of > the sample. > For a start, we can assume that every integer in my sample can assume > only the values 1, 2 and 3. > Any suggestion is appreciated. > Cheers > > Lorenzo > > ______________________________________________ > [hidden email] mailing list -- To UNSUBSCRIBE and more, see > 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. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Integer Sample with Mean Dependent on Size

 Yes, you are right (and yours is one of the possible cases). I think this works (I resorted to pen and paper for once) generate_k <- function(N, n3){     n1 <- 2+n3     n2 <- N-n1-n3     out <- c(rep(1, n1), rep(2, n2), rep(3, n3))     return(out) } where N is the length of the sample, n3 is the number of times I have the number 3 in the sample (n1 and n2 are the same for 1 and 2, respectively). So far it holds! L. On Thu, Aug 01, 2019 at 12:37:47PM +0200, Gerrit Eichner wrote: >n_1 + ... + n_N = 2(N-1) is requested for integers n_i >= 1. > >What about c(rep(2, N-2), 1, 1))? > >but I'm afraid that this was not what you really wanted. ;-) >However, you didn't say if your sample should be random. :-) > > Best regards  --  Gerrit > >--------------------------------------------------------------------- >Dr. Gerrit Eichner                   Mathematical Institute, Room 212 >[hidden email]   Justus-Liebig-University Giessen >Tel: +49-(0)641-99-32104          Arndtstr. 2, 35392 Giessen, Germany >http://www.uni-giessen.de/eichner>--------------------------------------------------------------------- > >Am 01.08.2019 um 12:27 schrieb Lorenzo Isella: >>Dear All, >>I cannot unfortunately provide any R code, otherwise I >>would not need to post this in the first place. >>I need to generate a sample of N positive non-zero >>integers such that their mean is *exactly* 2(N-1)/N, >>i.e. the mean depends on the length of the sample. >>For a start, we can assume that every integer in my >>sample can assume only the values 1, 2 and 3. >>Any suggestion is appreciated. >>Cheers >> >>Lorenzo >> >>______________________________________________ >>[hidden email] mailing list -- To UNSUBSCRIBE and more, see >>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. ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Integer Sample with Mean Dependent on Size

 In reply to this post by Lorenzo Isella 2(N-1)/N = 2 - 2/N. So one way to get exactly that mean is to make all the numbers 2 except for two of them which are 1. N < 2 : can't be done. N = 2 : only [1,1] does the job. N = 3 : the sum of the three numbers must be 4, so none of them         can be 3, so [1,1,2] [1,2,1] [2,1,1] are the only         possibilities. N = 4 : [1,1,1,3] [1,1,2,2] [1,1,3,1] [1,2,1,2] [1,2,2,1] [1,3,1,1] [2,1,1,2] [2,1,2,1] [2,2,1,1] [3,1,1,1] Is there a pattern here? Yes.  There must be an integer k such that 0 <= 2k <= N-2 and then you have a rearrangement of (k+2) 1s, (N-2-2k) 2s, and k 3s.         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.