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?
>
(1) you have a missing division by 4, but this doesn't really affect
the problem.
(2) not all skewness and kurtosis can arise .... try constructing your
mu, s2, etc.
from a given set of w,x,y,z and see if your procedure can find the
right answer when you know there really is one.
David Jones
.
.
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