RE: CV for exponential model

From:yaning@ufl.edu Subject:RE: [NMusers] CV for exponential model Date:Tue, 4 Feb 2003 17:18:49 -0500 I guess Luciane's confusion is about the exponential model. Basically, it is because of the FO(first order) method (first order Taylor expansion). If we assume V=theta*exp(eta) with eta~N(0, omega**2), V follows an exact lognormal distribution. But Taylor expansion at zero will yield V=theta+theta*eta approximately. In other words, V approximately follows a normal distribtuion with mean of theta and variance of theta**2*omega**2. Then CV of y is approximately sqrt(var(y))/mean(y)*100=theta*omega/theta*100=omega*100. I remember we learned this in two of our statistic courses, survival analysis and matrix algebra, something about the first order Delta method. If Y=f(X), Y=f(X0)+(X-X0)*f'(X0) and E(Y)=E(X) and Var(Y)=f'(X0)**2*Var(X) by Delta method which is based on first order Taylor expansion. Of course, if we assuem Y=theta*(1+eta), it is straightforward. Hope this helps Yaning Wang Department of Pharmaceutics College of Pharmacy University of Florida