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Estimation of the mean and standard deviation from normally distributed singly‐censored samples
Author(s) -
Aboueissa Abou ElMakarim A.,
Stoline Michael R.
Publication year - 2004
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.643
Subject(s) - standard deviation , statistics , maximum likelihood , mathematics , standard error , estimation , sample (material) , constant (computer programming) , mean value , computer science , chemistry , management , chromatography , economics , programming language
This article is concerned with the estimation of the mean μ and standard deviation σ utilizing a singly‐left‐censored sample of normally distributed data having a known detection limit (DL). A new computer algorithm for obtaining the Cohen (1959) maximum likelihood estimates of μ and σ is provided which does not require auxiliary tables. The algorithm utilizes S‐PLUS or R languages. Closed form estimates of the mean and standard deviation obtained under a new replacement method are given for normally distributed left‐censored samples, which appear to be superior to existing replacement method estimates. The replacement method estimates are based on replacing the left‐censored observations by a non‐constant value. The performances of these methods are compared utilizing many simulated data sets. Copyright © 2004 John Wiley & Sons, Ltd.