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Journal of Systems Science and Complexity

, Volume 30, Issue 6, pp 1350–1363 | Cite as

Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling

  • Wangxue ChenEmail author
  • Yi Tian
  • Minyu Xie
Article

Abstract

This paper studies a maximum likelihood estimator (MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling (RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed (iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice, are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.

Keywords

Complete sufficient statistic continuous one-parameter exponential family maximum likelihood estimator ranked set sampling 

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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsJishou UniversityJishouChina
  2. 2.Department of Mathematics and StatisticsCentral China Normal UniversityWuhanChina

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