Ordered Double Ranked Set Samples and Applications to Inference

SYNOPTIC ABSTRACT

Balakrishnan and Li (2005) introduced the use of ordered ranked set sampling (ORSS) and derived the best linear unbiased estimators (BLUEs) under ORSS (BLUEs-ORSS). In this study, we extend the work to ordered double ranked set sampling (ODRSS) scheme by using the idea of order statistics from independent and nonidentically distributed random variables. The BLUEs of the location and the scale parameters of a location-scale family of distributions are derived using ODRSS (BLUEs-ODRSS). It is shown that the BLUEs-ODRSS are uniformly better than the BLUEs-ORSS for the two-parameter exponential, normal, and generalized geometric distributions. Furthermore, we also study the properties of the distribution-free confidence intervals for quantiles and tolerance intervals based on ODRSS. We show that the confidence and tolerance intervals under the ODRSS scheme are more precise than their counterparts based on the ORSS scheme.

Key Words and Phrases::

• best linear unbiased estimator
• confidence interval
• order statistics
• ordered double ranked set samples
• relative efficiency

Acknowledgments

The authors are thankful to the Editor-in-Chief, Associate Editor, and anonymous referee(s) for their valuable comments and suggestions that led to an improved version of the article.