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BEHBOODIAN, J., ASGHARZADEH, A.. (1386). ON THE DISTRIBUTION OF Z-SCORES. , 32(1), 71-78. doi: 10.22099/ijsts.2008.2245
J. BEHBOODIAN; A. ASGHARZADEH. "ON THE DISTRIBUTION OF Z-SCORES". , 32, 1, 1386, 71-78. doi: 10.22099/ijsts.2008.2245
BEHBOODIAN, J., ASGHARZADEH, A.. (1386). 'ON THE DISTRIBUTION OF Z-SCORES', , 32(1), pp. 71-78. doi: 10.22099/ijsts.2008.2245
BEHBOODIAN, J., ASGHARZADEH, A.. ON THE DISTRIBUTION OF Z-SCORES. , 1386; 32(1): 71-78. doi: 10.22099/ijsts.2008.2245

ON THE DISTRIBUTION OF Z-SCORES

Iranian Journal of Science
مقاله 10، دوره 32، شماره 1، اردیبهشت 2008، صفحه 71-78    اصل مقاله (298.78 K)
نوع مقاله: Research Note
شناسه دیجیتال (DOI): 10.22099/ijsts.2008.2245
نویسندگان
J. BEHBOODIAN* 1؛ A. ASGHARZADEH2
1Department of Mathematics, Islamic Azad University, Shiraz, I. R. of Iran
2Department of Statistics, Faculty of Basic Sciences, Mazandaran University, Babolsar, I. R. of Iran
چکیده
Let X ,..., Xn 1 be a random sample from a distribution with sample mean X and sample
variance 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 underlying
normal 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.
کلیدواژه‌ها
Finite exchangeability؛ grading؛ outlier test؛ Quadratic Forms؛ Thompson's identity؛ Samuelson's inequality؛ Slutsky's theorem
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