A Note on the Accuracy of Normal Approximation of Random Quantities. Issue 1 (May 2021)

• Record Type: Journal Article
• Authors: Ahmad, Ibrahim A.; Mugdadi, A. R.
• Is Part Of: Calcutta Statistical Association bulletin. Volume 73:Issue 1(2021)
• Page Start: 62
• Page End: 67
• Publication Date: 2021-05
• Subjects: Sample quantities -- Asymptotic normality -- rates of convergence -- random sample; Mathematical statistics -- Periodicals; Statistics -- Methodology -- Periodicals; Statistics -- Periodicals; 519.5
• DOI: 10.1177/00080683211013510
• Languages: English
• ISSNs: 0008-0683

Abstract

For a sequence of independent, identically distributed random variable (iid rv's){ X n } and a sequence of integer-valued random variables{ N n }, define the random quantiles asξ ̂ N n, p = X ( [ N n p ] + 1 ), where[ x ] denote the largest integer less than or equal tox, andX ( i ) thei th order statistic in a sampleX 1, X 2, . . ., X n and0 ≤ p ≤ 1 . In this note, the limiting distribution and its exact order approximation are obtained forξ ̂ N n, p . The limiting distribution result we obtain extends the work of several including Wretman [ 1 ] . The exact order of normal approximation generalizes the fixed sample size results of Reiss [ 2 ] . AMS 2000 subject classification: 60F12; 60F05; 62G30.