Chee Chen
2011-Apr-22 13:59 UTC
[R] How to generate normal mixture random variables with given covariance function
Dear All, Suppose Z_i, i=1,...,m are marginally identically distributed as a two normal mixture p0*N(0,1) + (1-p0) *N( miu_i, 1) where miu_i are identically distributed according to a mixture and I have generated Z_i one by one . Now suppose these m random variables are jointly m-dimensional normal with correlation matrix M= (m_ij). How to proceed next or how to start correctly ? Question: 1. Are Z_i, i=1,...,m I have generated jointly normal? 2. How to get them such that they are jointly normal with M Thank you, -Chee [[alternative HTML version deleted]]
Giovanni Petris
2011-Apr-22 14:50 UTC
[R] How to generate normal mixture random variables with given covariance function
On Fri, 2011-04-22 at 09:59 -0400, Chee Chen wrote:> Dear All, > Suppose Z_i, i=1,...,m are marginally identically distributed as a two > normal mixture p0*N(0,1) + (1-p0) *N( miu_i, 1) where miu_i are > identically distributed according to a mixture and I have generated > Z_i one by one . > > Now suppose these m random variables are jointly m-dimensional normalThis is not related to R, so you should probably ask the question somewhere else. The short answer is that the Z_i cannot be jointly Normally distributed, since they are not marginally Normally distributed. Giovanni Petris> with correlation matrix M= (m_ij). > How to proceed next or how to start correctly ? > > Question: > 1. Are Z_i, i=1,...,m I have generated jointly normal? > 2. How to get them such that they are jointly normal with M > > Thank you, > -Chee > [[alternative HTML version deleted]] > > ______________________________________________ > 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.-- Giovanni Petris <GPetris at uark.edu> Associate Professor Department of Mathematical Sciences University of Arkansas - Fayetteville, AR 72701 Ph: (479) 575-6324, 575-8630 (fax) http://definetti.uark.edu/~gpetris/