Rich Strauss wrote:
>
> At 09:00 AM 4/2/2003 -0400, Robert Dawson wrote:
>
> > 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?
As I'm sure you're aware, your g1 and g2 are not skewness and kurtosis,
but need scaling by the 3/2 and 2nd powers of s2 respectively. I mention
this because IIRC not all (skewness,kurtosis) pairs are possible;
and it may be harder to determine which ones *are* possible with a
nonstandard representation ofthe quadruple (mu,s2,g1,g2).
-Robert Dawson
.
.
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