Dear Allstat,
I am currently comparing the results of a survey carried out last year with
a very similar survey ten years before. The problem is that I only have a
very brief summary of the old set of results and therefore I am
having/hoping to use the range of the variables as a surrogate for their
variances. Can anyone reccomend any references for this? So far all I've
managed to get out is the joint distribution of
range r= X(n) - X(1)
location l= 1/2(X(1)+X(n))
(sample size n)
g(r,l)= n!/2 f(1/2r+l)f(-1/2r+l)[ F(1/2r+l)-F(-1/2r+l)]^(n-2)
where g is the pdf of r & l, f is the pdf of the iidrv X1...Xn and F their
cdf, and X(i) is the ith member of the ordered set of X's.
I can numerically evaluate the expectation and variance of r, for specific
distributions and sample sizes, but are there any assymptotic results such
as a limit as n tends to infinity of E(r) or does g(r) tend to a
distribution?
Any help is gratefully received.
Simon Bond
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|