Hi all, I have n independent variables A_1, A_2, A_3,......,A_n, and each with known variances var(A_1), var(A_2),..., but unknown mean. How can I get the approximation of the variance of the product of the variables using numerical computation, i.e. var(A_1*A_2*A_3*.....*A_n)? Thanks. Sincerely, Yanwei Zhang Department of Actuarial Research and Modeling Munich Re America Tel: 609-275-2176 Email: yzhang@munichreamerica.com<mailto:yzhang@munichreamerica.com> [[alternative HTML version deleted]]
If it is in a data frame with the variables as columns try f <- cbind(a*b, b*c, c*d) sapply(f, function(x)var(x)) On Fri, Jul 25, 2008 at 5:06 PM, Zhang Yanwei - Princeton-MRAm < YZhang@munichreamerica.com> wrote:> Hi all, > I have n independent variables A_1, A_2, A_3,......,A_n, and each with > known variances var(A_1), var(A_2),..., but unknown mean. How can I get the > approximation of the variance of the product of the variables using > numerical computation, i.e. var(A_1*A_2*A_3*.....*A_n)? Thanks. > > Sincerely, > Yanwei Zhang > Department of Actuarial Research and Modeling > Munich Re America > Tel: 609-275-2176 > Email: yzhang@munichreamerica.com<mailto:yzhang@munichreamerica.com> > > > [[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. >-- Let's not spend our time and resources thinking about things that are so little or so large that all they really do for us is puff us up and make us feel like gods. We are mammals, and have not exhausted the annoying little problems of being mammals. -K. Mullis [[alternative HTML version deleted]]
On 25-Jul-08 21:06:38, Zhang Yanwei - Princeton-MRAm wrote:> Hi all, > I have n independent variables A_1, A_2, A_3,......,A_n, and each > with known variances var(A_1), var(A_2),..., but unknown mean. How can > I get the approximation of the variance of the product of the variables > using numerical computation, i.e. var(A_1*A_2*A_3*.....*A_n)? Thanks.Without knowing the means, you cannot. Let M1, M2, ... , Mn be the means of A1, A2, ... , An, and let V1, V23, ..., Vn be their variances. Then (to a first approximation) Var(A1*A2*...*An) = (M1^2)*(M2^2)*...*(Mn^2) * (V1/(M1^2) + V2/(M2^2) + ... + Vn/(Mn^2)) so the variance depends on the means Mi as well as on the variances Vi. Ted. -------------------------------------------------------------------- E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk> Fax-to-email: +44 (0)870 094 0861 Date: 25-Jul-08 Time: 22:47:56 ------------------------------ XFMail ------------------------------
On 25/07/2008 5:06 PM, Zhang Yanwei - Princeton-MRAm wrote:> Hi all, > I have n independent variables A_1, A_2, A_3,......,A_n, and each with known variances var(A_1), var(A_2),..., but unknown mean. How can I get the approximation of the variance of the product of the variables using numerical computation, i.e. var(A_1*A_2*A_3*.....*A_n)? Thanks.You can't, in any reasonable sense. The variance depends strongly on the means, which you say you don't have. If you want to be unreasonable, then the answer is that the variance is approximately 1. Duncan Murdoch