Information Theoretic Weighted Mean Based on Truncated Ranked Set Sampling

Abstract

This article proposes using an information theoretic procedure in order to obtain an unbiased weighted mean estimator for the population mean when the data collection structure is truncated-based ranked set sampling. The performance of the proposed estimator is discussed along with its properties, and the optimal weights are computed by maximizing Shannon’s entropy. It is found that the weighted truncated-based ranked set sampling estimator is more accurate and more efficient than its unweighted counterpart or the simple random sampling-based estimators.

AMS Subject Classification:

• 62G05

Keywords:

• Maximum Entropy
• Ranked Set Sampling
• Relative Efficiency
• Shannon’s Entropy