Dixon Statistical test

[mpv55]

Recently, I was reading the Dixon (Annals Math. Stat. 22, (1951) 68-78) method for extreme (outliers) values. He considered that there are n ordered values (x1, x2, ...xn) of an analytical measurement. The values belong to a normal distribution. He defined two equations:
1. For Critical value

r01=\frac{xn-xn-1}{xn-x1}


2. The density function for x1, xn-1, xn is

\frac{n!}{(n-3)!}f(x1)dx1(\ointx1xn-1f(t)dt)n-3 f(xn-1)dxn-1f(xn) dxn

I will appreciate if someone explains the derivation of the density function or site some reference which explains it.

Thanks

[Stephen Tashi]

Mixing in the "SUB" tag in between LaTex expressions seems to screw up the LaTex display. I can't make out what the density function is supposed to be. Can you revise it using the underscore ? (such as using the notation x_{n-1} for x with a subscript of n-1).