Dixon Statistical Test: Deriving Density Function

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SUMMARY

The discussion focuses on the Dixon Statistical Test for identifying extreme values in a normal distribution, specifically referencing the original work by Dixon in the Annals of Mathematical Statistics. The critical value is defined by the equation r01 = (xn - xn-1) / (xn - x1). Additionally, the density function for the ordered values x1, xn-1, and xn is expressed through a complex formula involving factorials and integrals. Participants seek clarification on the derivation of the density function and suggest formatting improvements for LaTeX expressions.

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  • Understanding of statistical methods for outlier detection
  • Familiarity with normal distribution properties
  • Knowledge of LaTeX formatting for mathematical expressions
  • Basic calculus, particularly integration techniques
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Statisticians, data analysts, and researchers focused on outlier detection and statistical methods in normal distributions will benefit from this discussion.

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=[tex]\frac{x<sub>n</sub>-x<sub>n-1</sub>}{x<sub>n</sub>-x<sub>1</sub>}[/tex]


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

[tex]\frac{n!}{(n-3)!}[/tex]f(x1)dx1([tex]\oint<sub>x<sub>1</sub></sub><sup>x<sub>n</sub>-1</sup>f(t)dt[/tex])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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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).
 

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