Parametric estimation of location and scale parameters based on ranked set sampling with unequal set sizes

Abstract

Ranked set sampling with unequal set sizes (RSSU) are some of the important variants of ranked set sampling with equal set sizes (RSS). The sets that arise naturally in many applications are typically of different set sizes. One may prefer to use the largest sets available naturally along with the smaller sets rather than an attempt to form artificial equal-sized sets. This article develops maximum likelihood estimators for the location-scale family of distributions based on ranked set sampling with unequal set sizes (RSSU). The closed form expressions for MLE under RSSU do not exist, we have proved the existence of MLE for location and scale parameters for some standard distributions for RSSU data. It is proved that MLE based on MedRSSU are more efficient than their counterparts based on SRS for some standard distributions for location-scale parameters. It is also shown that asymptotic efficiencies of the MLE based on MedRSSU are considerably better than those of the estimators based on RSS with the same number of observations. A simulation study is conducted to compare the performances of the MLE’s from RSS and MedRSSU with the corresponding SRS estimators when the underlying distributions are normal and logistic.

Keywords:

• Asymptotic relative efficiency
• Fisher information matrix
• Location-scale family of distributions
• Maximum likelihood estimation
• MedRanked set sampling with unequal samples
• Ranked set sampling
• Ranked set sampling with unequal samples
• Simple random sample

Acknowledgement

The author thank the Editors and anonymous reviewers for making some valuable suggestions which led to a considerable improvement in the presentation of this manuscript.