Modified maximum likelihood estimators using ranked set sampling


Balci S., Akkaya A., Ulgen B. E.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.238, pp.171-179, 2012 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 238
  • Publication Date: 2012
  • Doi Number: 10.1016/j.cam.2012.08.030
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.171-179
  • Keywords: Order statistics, Modified maximum likelihood, Ranked set sampling, ROBUST ESTIMATION, PARAMETERS

Abstract

The closed-form maximum likelihood estimators (MLEs) of population mean and variance under ranked set sampling (RSS) do not exist since the likelihood equations involve nonlinear functions and have usually no explicit solutions. We derive modified maximum likelihood (MML) estimators for the population mean and variance under RSS and show that they are considerably more efficient than RSS estimators. Furthermore, we suggest two new estimators for the unknown parameters using two modified ranked set sampling methods and show that these methods make the variances of both MML and RSS estimators smaller. (C) 2012 Elsevier B.V. All rights reserved.