I think that four data will suffice for any possible combination of mean,SD,skewness and kurtosis. Just write out the equations, expanding all summations:
mu = w + x + y + z sigma^2 = (w-mu)^2 + (x-mu)^2 + (y-mu^2) + (z-mu)^2 / 4 (etc)
and solve.
-Robert Dawson
I thought that this was such a cool idea that I decided to try it. Since I'm not about to trust my own ability to solve those simultaneous equations, I used Matlab's 'solve' function:
mu = 5;
s2 = 3;
g1 = 2;
g2 = 5; eq1 = sprintf('w+x+y+z=%f',mu)
eq2 = sprintf('(w-%f)^2+(x-%f)^2+(y-%f)^2+(z-%f)^2=%f',mu,mu,mu,mu,s2)
eq3 = sprintf('(w-%f)^3+(x-%f)^3+(y-%f)^3+(z-%f)^3=%f',mu,mu,mu,mu,g1)
eq4 = sprintf('(w-%f)^4+(x-%f)^4+(y-%f)^4+(z-%f)^4=%f',mu,mu,mu,mu,g2)[w,x,y,z] = solve(eq1,eq2,eq3,eq4)
However, the resulting values are always complex. I've played around quite a bit with it and can't seem to figure out what's going on, except that it's undoubtedly the roots that are causing the problem. Any ideas?
Rich Strauss
============================================================= Richard E. Strauss (806) 742-2719 Biological Sciences (806) 742-2963 Fax Texas Tech University [EMAIL PROTECTED] Lubbock, TX 79409-3131 <http://www.biol.ttu.edu/Strauss/Strauss.html> =============================================================
. . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
