@article { author = {BEHBOODIAN, J. and ASGHARZADEH, A.}, title = {ON THE DISTRIBUTION OF Z-SCORES}, journal = {Iranian Journal of Science}, volume = {32}, number = {1}, pages = {71-78}, year = {2008}, publisher = {Springer}, issn = {2731-8095}, eissn = {2731-8109}, doi = {10.22099/ijsts.2008.2245}, abstract = {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.}, keywords = {Finite exchangeability,grading,outlier test,Quadratic Forms,Thompson's identity,Samuelson's inequality,Slutsky's theorem}, url = {https://ijsts.shirazu.ac.ir/article_2245.html}, eprint = {https://ijsts.shirazu.ac.ir/article_2245_7c4086e2bf5cb1aaec28c2c0824b1b6e.pdf} }