TY - JOUR
ID - 2245
TI - ON THE DISTRIBUTION OF Z-SCORES
JO - Iranian Journal of Science and Technology (Sciences)
JA - IJSTS
LA - en
SN - 1028-6276
AU - BEHBOODIAN, J.
AU - ASGHARZADEH, A.
AD - Department of Mathematics, Islamic Azad University, Shiraz, I. R. of Iran
AD - Department of Statistics, Faculty of Basic Sciences, Mazandaran University, Babolsar, I. R. of Iran
Y1 - 2008
PY - 2008
VL - 32
IS - 1
SP - 71
EP - 78
KW - Finite exchangeability
KW - grading
KW - outlier test
KW - Quadratic Forms
KW - Thompson's identity
KW - Samuelson's
inequality
KW - Slutsky's theorem
DO - 10.22099/ijsts.2008.2245
N2 - 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.
UR - http://ijsts.shirazu.ac.ir/article_2245.html
L1 - http://ijsts.shirazu.ac.ir/article_2245_7c4086e2bf5cb1aaec28c2c0824b1b6e.pdf
ER -