HAKAN DEMIRTAS wrote: > I can't seem to get computationally stable estimates for the following system: > > Y=a+bX+cX^2+dX^3, where X~N(0,1). (Y is expressed as a linear combination of > the first three powers of a standard normal variable.) Assuming that E(Y)=0 > and Var(Y)=1, one can obtain the following equations after tedious algebraic > calculations: > > 1) b^2+6bd+2c^2+15d^2=1 > 2) 2c(b^2+24bd+105d^2+2)=E(Y^3) > 3) 24[bd+c^2(1+b^2+28bd)+d^2(12+48bd+141c^2+225d^2)]=E(Y^4)-3 > > Obviously, a=-c. Suppose that distributional form of Y is given so we know > E(Y^3) and E(Y^4). In other words, we have access to the third and fourth raw > moments. How do we solve for these four coefficients? I reduced the number of > unknowns/equations to two, and subsequently used a grid approach. It works > well when I am close to the center of the support, but fails miserably at the > tails. Any ideas? Hopefully, there is a nice R function that does this. > > Hakan Demirtas > > > [[alternative HTML version deleted]] > > ______________________________________________ > R-devel@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel > This is really a question for r-help not r-devel.
I was about to say that this was a question for a symbolic algebra system, but first tried in MuPAD 4.0, and left the machine alone. returning after 2 hours MuPAD was still grinding and I had to kill it. Kjetil ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
