I am trying to determine if a given sample comes from a Normal distribution. For that purpose I want to perform a Shapiro-Wilk test in the way stated on wikipedia. My concern comes with the vector $(a_1,\dots,a_n)$, whose computation requires the knowledge of the expected values $(m_1,\dots,m_n)$ for the order statistics. I have no clue of what is this nor how I could compute it. I know what a statistic is and what expectation is, but I'm having a hard time trying to find any insight on this specific ones. Any help would be most aprreciate.
2026-03-27 04:15:16.1774584916
Shapiro-Wilk test
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I answer my own question: regardless of how the $a_i$ are calculated, there exist tables with their approximate values for certain parameters, something that was unknown to me.
Here's a link to some examples: http://www.real-statistics.com/tests-normality-and-symmetry/statistical-tests-normality-symmetry/shapiro-wilk-test/