Czarek Kowalski
2017-May-09 20:11 UTC
[R] Generating samples from truncated multivariate Student-t distribution
Of course I have expected the difference between theory and a sample of realizations of RV's and result mean should still be a random variable. But, for example for 4th element of mean vector: 35.31 - 34.69571 = 0.61429. It is quite big difference, nieprawda?? I have expected that the difference would be smaller because of law of large numbers (for 10mln samples the difference is quite similar). On 9 May 2017 at 21:40, David Winsemius <dwinsemius at comcast.net> wrote:> >> On May 9, 2017, at 10:09 AM, Czarek Kowalski <czarek230800 at gmail.com> wrote: >> >> Dear Members, >> I am working with 6-dimensional Student-t distribution with 4 degrees >> of freedom truncated to [20; 60]. I have generated 100 000 samples >> from truncated multivariate Student-t distribution using rtmvt >> function from package ?tmvtnorm?. I have also calculated mean vector >> using equation (3) from attached pdf. The problem is, that after >> summing all elements in one column of rtmvt result (and dividing by >> 100 000) I do not receive the same result as using (3) equation. Could >> You tell me, what is incorrect, why there is a difference? > > I guess the question is why you would NOT expect a difference between theory and a sample of realizations of RV's? The result mean should still be a random variable, night wahr? > > >> Yours faithfully >> Czarek Kowalski >> <truncatedT.pdf>______________________________________________ >> R-help at r-project.org 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. > > David Winsemius > Alameda, CA, USA >
David Winsemius
2017-May-09 20:17 UTC
[R] Generating samples from truncated multivariate Student-t distribution
> On May 9, 2017, at 1:11 PM, Czarek Kowalski <czarek230800 at gmail.com> wrote: > > Of course I have expected the difference between theory and a sample > of realizations of RV's and result mean should still be a random > variable. But, for example for 4th element of mean vector: 35.31 - > 34.69571 = 0.61429. It is quite big difference, nieprawda?? I have > expected that the difference would be smaller because of law of large > numbers (for 10mln samples the difference is quite similar).I for one have no idea what is meant by a "4th element of mean vector". So I have now idea what to consider "big". I have found that my intuitions about multivariate distributions, especially those where the covariate structure is as complex as you have assumed, are often far from simulated results. I suggest you post some code and results. -- David.> > On 9 May 2017 at 21:40, David Winsemius <dwinsemius at comcast.net> wrote: >> >>> On May 9, 2017, at 10:09 AM, Czarek Kowalski <czarek230800 at gmail.com> wrote: >>> >>> Dear Members, >>> I am working with 6-dimensional Student-t distribution with 4 degrees >>> of freedom truncated to [20; 60]. I have generated 100 000 samples >>> from truncated multivariate Student-t distribution using rtmvt >>> function from package ?tmvtnorm?. I have also calculated mean vector >>> using equation (3) from attached pdf. The problem is, that after >>> summing all elements in one column of rtmvt result (and dividing by >>> 100 000) I do not receive the same result as using (3) equation. Could >>> You tell me, what is incorrect, why there is a difference? >> >> I guess the question is why you would NOT expect a difference between theory and a sample of realizations of RV's? The result mean should still be a random variable, night wahr? >> >> >>> Yours faithfully >>> Czarek Kowalski >>> <truncatedT.pdf>______________________________________________ >>> R-help at r-project.org 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. >> >> David Winsemius >> Alameda, CA, USA >>David Winsemius Alameda, CA, USA
Czarek Kowalski
2017-May-09 21:05 UTC
[R] Generating samples from truncated multivariate Student-t distribution
I have already posted that in attachement - pdf file. I am posting plain text here:> library(tmvtnorm)> meann = c(55, 40, 50, 35, 45, 30)> covv = matrix(c( 1, 1, 0, 2, -1, -1,+ 1, 16, -6, -6, -2, 12, + 0, -6, 4, 2, -2, -5, + 2, -6, 2, 25, 0, -17, + -1, -2, -2, 0, 9, -5, + -1, 12, -5, -17, -5, 36), 6, 6)> df = 4> lower = c(20, 20, 20, 20, 20, 20)> upper = c(60, 60, 60, 60, 60, 60)> X1 <- rtmvt(n=100000, meann, covv, df, lower, upper)> sum(X1[,1]) / 100000[1] 54.98258> sum(X1[,2]) / 100000[1] 40.36153> sum(X1[,3]) / 100000[1] 49.83571> sum(X1[,4]) / 100000[1] 34.69571 # "4th element of mean vector"> sum(X1[,5]) / 100000[1] 44.81081> sum(X1[,6]) / 100000[1] 31.10834 And corresponding results received using equation (3) from pdf file: [54.97, 40, 49.95, 35.31, # "4th element of mean vector" 44.94, 31.32] On 9 May 2017 at 22:17, David Winsemius <dwinsemius at comcast.net> wrote:> >> On May 9, 2017, at 1:11 PM, Czarek Kowalski <czarek230800 at gmail.com> wrote: >> >> Of course I have expected the difference between theory and a sample >> of realizations of RV's and result mean should still be a random >> variable. But, for example for 4th element of mean vector: 35.31 - >> 34.69571 = 0.61429. It is quite big difference, nieprawda?? I have >> expected that the difference would be smaller because of law of large >> numbers (for 10mln samples the difference is quite similar). > > I for one have no idea what is meant by a "4th element of mean vector". So I have now idea what to consider "big". I have found that my intuitions about multivariate distributions, especially those where the covariate structure is as complex as you have assumed, are often far from simulated results. > > I suggest you post some code and results. > > -- > David. > > >> >> On 9 May 2017 at 21:40, David Winsemius <dwinsemius at comcast.net> wrote: >>> >>>> On May 9, 2017, at 10:09 AM, Czarek Kowalski <czarek230800 at gmail.com> wrote: >>>> >>>> Dear Members, >>>> I am working with 6-dimensional Student-t distribution with 4 degrees >>>> of freedom truncated to [20; 60]. I have generated 100 000 samples >>>> from truncated multivariate Student-t distribution using rtmvt >>>> function from package ?tmvtnorm?. I have also calculated mean vector >>>> using equation (3) from attached pdf. The problem is, that after >>>> summing all elements in one column of rtmvt result (and dividing by >>>> 100 000) I do not receive the same result as using (3) equation. Could >>>> You tell me, what is incorrect, why there is a difference? >>> >>> I guess the question is why you would NOT expect a difference between theory and a sample of realizations of RV's? The result mean should still be a random variable, night wahr? >>> >>> >>>> Yours faithfully >>>> Czarek Kowalski >>>> <truncatedT.pdf>______________________________________________ >>>> R-help at r-project.org 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. >>> >>> David Winsemius >>> Alameda, CA, USA >>> > > David Winsemius > Alameda, CA, USA >