Cumulative Tsallis Entropy for Maximum Ranked Set Sampling with Unequal Samples

TL;DR

This paper investigates the information content of maximum ranked set sampling with unequal samples using Tsallis entropy, providing bounds, properties, and comparisons with simple random sampling.

Contribution

It introduces new bounds and properties of Tsallis entropy for MRSSU and compares its information content with SRS, offering novel insights into sampling uncertainty.

Findings

Tsallis entropy bounds for MRSSU derived

Monotonic properties and stochastic orders established

Comparison shows differences in information content between MRSSU and SRS

Abstract

In this paper, we consider the information content of maximum ranked set sampling procedure with unequal samples (MRSSU) in terms of Tsallis entropy which is a nonadditive generalization of Shannon entropy. We obtain several results of Tsallis entropy including bounds, monotonic properties, stochastic orders, and sharp bounds under some assumptions. We also compare the uncertainty and information content of MRSSU with its counterpart in the simple random sampling (SRS) data. Finally, we develop some characterization results in terms of cumulative Tsallis entropy and residual Tsallis entropy of MRSSU and SRS data.