%0 Journal Article
%T ON THE DISTRIBUTION OF Z-SCORES
%J Iranian Journal of Science and Technology (Sciences)
%I Springer
%Z 1028-6276
%A BEHBOODIAN, J.
%A ASGHARZADEH, A.
%D 2008
%\ 02/17/2008
%V 32
%N 1
%P 71-78
%! ON THE DISTRIBUTION OF Z-SCORES
%K Finite exchangeability
%K grading
%K outlier test
%K Quadratic Forms
%K Thompson's identity
%K Samuelson's
inequality
%K Slutsky's theorem
%R 10.22099/ijsts.2008.2245
%X Let X ,..., Xn 1 be a random sample from a distribution with sample mean X and samplevariance S 2. In this paper we consider certain very general properties of the so-called “Z-scores”X X S i n i ( − )/ : = 1,...., . A representation theorem is then given for Z-scores obtained from an underlyingnormal population, together with a theorem for their limiting distribution as the sample size tends to infinity.Finally, two applications involving grading and testing for an outlier are presented.
%U http://ijsts.shirazu.ac.ir/article_2245_7c4086e2bf5cb1aaec28c2c0824b1b6e.pdf