Maximum likelihood estimator of the shape parameter under simple random sampling and moving extremes ranked set sampling

• Published in: Statistics & probability letters Vol. 226; p. 110465
• Main Authors: Yang, Rui, Chen, Wangxue
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2025
• Subjects: Fisher information number; Maximum likelihood estimator; Moving extremes ranked set sampling; Shape parameter; Maximum likelihood estimator; Shape parameter; 62F10; Fisher information number; 62D05; Moving extremes ranked set sampling
• ISSN: 0167-7152
• DOI: 10.1016/j.spl.2025.110465

This paper examines the maximum likelihood estimator (MLE) for the shape parameter from the shape family, focusing on both simple random sampling (SRS) and moving extremes ranked set sampling (MERSS). The study establishes the existence and uniqueness of the MLE for several common shape distributions. In order to give more insight into the performance of MERSS with respect to (w.r.t.) SRS, the asymptotic efficiency of the MLE using MERSS w.r.t. that using SRS is computed for the common shape distributions. The findings from the common shape distributions indicate that MERSS provides a more efficient approach for estimating the shape parameter compared to SRS. Additionally, we examine the implications of imperfect ranking.