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On General Weighted Extropy of Extreme Ranked Set Sampling

Pradeep Kumar Sahu, Nitin Gupta

Abstract

The extropy measure, introduced by Lad, Sanfilippo, and Agro in their (2015) paper in Statistical Science, has garnered significant interest over the past years. In this study, we present a novel representation for the weighted extropy within the context of extreme ranked set sampling. Additionally, we offer related findings such as stochastic orders, characterizations, and precise bounds. Our results shed light onthe comparison between the weighted extropy of extreme ranked set sampling and its counterpart in simple random sampling.

On General Weighted Extropy of Extreme Ranked Set Sampling

Abstract

The extropy measure, introduced by Lad, Sanfilippo, and Agro in their (2015) paper in Statistical Science, has garnered significant interest over the past years. In this study, we present a novel representation for the weighted extropy within the context of extreme ranked set sampling. Additionally, we offer related findings such as stochastic orders, characterizations, and precise bounds. Our results shed light onthe comparison between the weighted extropy of extreme ranked set sampling and its counterpart in simple random sampling.
Paper Structure (5 sections, 12 theorems, 27 equations)

This paper contains 5 sections, 12 theorems, 27 equations.

Table of Contents

  1. Introduction
  2. Some results on GWE and related properties
  3. General Weighted Extropies of ERSS
  4. Characterization results
  5. Stochastic comparision

Key Result

Theorem 3.1

Let $X$ be a non-negative absolutely continuous random variable with pdf f and cdf F. Assume $\eta(x)$ is an increasing function and $\frac{w_1(\eta(x))}{\eta^\prime (x)} \leq (\geq) w_1(x)$ and $\eta(0)=0$. If $V=\eta(X)$, then $J^{w_1}(\textbf{X}_{ERSS}^{(n)})\leq (\geq) J^{w_1}(\textbf{V}_{ERSS}^

Theorems & Definitions (19)

  • Definition 1
  • Definition 2
  • Example 3.1
  • Example 3.2
  • Example 3.3
  • Theorem 3.1
  • Example 3.4
  • Theorem 3.2
  • Lemma 4.1
  • Theorem 4.1
  • ...and 9 more