Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Extropy and Varextropy estimators with applications

Santosh Kumar Chaudhary, Nitin Gupta

Abstract

In many statistical studies, the measure of uncertainties like entropy, extropy, varentropy and varextropy of a distribution function is of prime interest. This paper proposes estimators of extropy and varextropy. Proposed estimators are consistent. Based on extropy estimator, a test of symmetry is given. The proposed test has the advantage that we do not need to estimate the centre of symmetry. The critical value and power of the proposed test statistics have been obtained. The test procedure has been implemented on six real-life data sets to verify its performance in identifying the symmetric nature.

Extropy and Varextropy estimators with applications

Abstract

In many statistical studies, the measure of uncertainties like entropy, extropy, varentropy and varextropy of a distribution function is of prime interest. This paper proposes estimators of extropy and varextropy. Proposed estimators are consistent. Based on extropy estimator, a test of symmetry is given. The proposed test has the advantage that we do not need to estimate the centre of symmetry. The critical value and power of the proposed test statistics have been obtained. The test procedure has been implemented on six real-life data sets to verify its performance in identifying the symmetric nature.
Paper Structure (16 sections, 16 theorems, 45 equations)

This paper contains 16 sections, 16 theorems, 45 equations.

Table of Contents

  1. Introduction
  2. Varextropy
  3. Weighted varextropy
  4. Varextropy Estimators
  5. The first estimator
  6. The second estimator
  7. The third estimator
  8. The fourth estimator
  9. The fifth estimator
  10. The sixth estimator
  11. A Characterization of Uniform distribution
  12. Test of symmetry using extropy
  13. Critical values
  14. Power and size of test
  15. Real data application
  16. ...and 1 more sections

Key Result

Proposition 1

Let $X\leq_{disp} Y$ then $VJ(U_n^X) \geq VJ(U_n^Y).$

Theorems & Definitions (22)

  • Example 1
  • Example 2
  • Example 3
  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Remark 1
  • Example 4
  • Example 5
  • Theorem 1
  • ...and 12 more