Dear all, This is a pure statistical question, not necessarly related to R. I could not find it in literature. Suppose I'm intersted in a parameter rho, say, equal to: r=beta1/beta2, where beta1 and beta2 come from a linear model y=beta0+beta1X1+beta2X2+.... Fitting the model I can get the (biased) estimate of r=b1/b2, where b1 and b2 are the estimates in the regression model; I can get the unbiased estimate of rho as well as its SE using the delta method. I'm interested in confidence interval for r. A simple method could be (I suppose) the classical one, i.e. using the standard gaussian quantiles: r +/- 1.96*SE. However because the ratio of two independent normal distribution is a Chaucy distribution I was thinking about an "exact methods". But the Chaucy distribution has not mean!!! My question is 1)If b1 and b2 are independent (X1 and X2 orthogonal) which is the sense of r and SE if the Chaucy distribution has not moments? 2) b1 and b2 are normal but not independent, their exact distribution is even Chaucy? 3)After all, is it correct use gaussian quantiles: r +/- 1.96*SE (as n goes inf, of course) hope to have been clear, hope in some your advice best vito -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
On 21 Dec 01, at 13:55, MUGGEO VITO wrote:> Dear all, > This is a pure statistical question, not necessarly related to R. > I could not find it in literature.<<<SNIP>>>> However because the ratio of two independent normal distribution is a Chaucy > distribution I was thinking about an "exact methods". But the Chaucy > distribution has not mean!!!Well, the ratio of two independent -standard- normals --- i.e., N(0,1) variables --- is distributed as Cauchy. But the heavy tails of the Cauchy arise from dividing by numbers close to 0. So, if the denominator of your ratio is distributed as, say, N(100, 1), then the ratio isn't going to look much like a Cauchy. ---JRG John R. Gleason Syracuse University 430 Huntington Hall Voice: 315-443-3107 Syracuse, NY 13244-2340 USA FAX: 315-443-4085 PGP public key at keyservers -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._