Email discussion lists for the UK Education and Research communities

## allstat@JISCMAIL.AC.UK

#### View:

 Message: [ First | Previous | Next | Last ] By Topic: [ First | Previous | Next | Last ] By Author: [ First | Previous | Next | Last ] Font: Monospaced Font

#### Options

Subject:

range distribution

From:

Simon Bond

Date:

Thu, 07 Jan 1999 16:38:25 +0000

Content-Type:

text/plain

Parts/Attachments:

 text/plain (33 lines)
 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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%