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mpv55
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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{x<sub>n</sub>-x<sub>n-1</sub>}{x<sub>n</sub>-x<sub>1</sub>}
2. The density function for x1, xn-1, xn is
\frac{n!}{(n-3)!}f(x1)dx1(\oint<sub>x<sub>1</sub></sub><sup>x<sub>n</sub>-1</sup>f(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
1. For Critical value
r01=\frac{x<sub>n</sub>-x<sub>n-1</sub>}{x<sub>n</sub>-x<sub>1</sub>}
2. The density function for x1, xn-1, xn is
\frac{n!}{(n-3)!}f(x1)dx1(\oint<sub>x<sub>1</sub></sub><sup>x<sub>n</sub>-1</sup>f(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
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