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Weighted cumulative residual Entropy Generating Function and its properties

Smitha S., Sudheesh K. Kattumannil, Sreedevi E. P

Abstract

The study on the generating function approach to entropy become popular as it generates several well-known entropy measures discussed in the literature. In this work, we define the weighted cumulative residual entropy generating function (WCREGF) and study its properties. We then introduce the dynamic weighted cumulative residual entropy generating function (DWCREGF). It is shown that the DWCREGF determines the distribution uniquely. We study some characterization results using the relationship between the DWCREGF and the hazard rate and/or the mean residual life function. Using a characterization based on DWCREGF, we develop a new goodness fit test for Rayleigh distribution. A Monte Carlo simulation study is conducted to evaluate the proposed test. Finally, the test is illustrated using two real data sets.

Weighted cumulative residual Entropy Generating Function and its properties

Abstract

The study on the generating function approach to entropy become popular as it generates several well-known entropy measures discussed in the literature. In this work, we define the weighted cumulative residual entropy generating function (WCREGF) and study its properties. We then introduce the dynamic weighted cumulative residual entropy generating function (DWCREGF). It is shown that the DWCREGF determines the distribution uniquely. We study some characterization results using the relationship between the DWCREGF and the hazard rate and/or the mean residual life function. Using a characterization based on DWCREGF, we develop a new goodness fit test for Rayleigh distribution. A Monte Carlo simulation study is conducted to evaluate the proposed test. Finally, the test is illustrated using two real data sets.
Paper Structure (7 sections, 8 theorems, 56 equations, 4 tables)

This paper contains 7 sections, 8 theorems, 56 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Weighted cumulative residual entropy generating function
  3. Dynamic weighted cumulative residual entropy generating function
  4. Test for Rayleigh distribution
  5. Simulation Studies
  6. Data Analysis
  7. Conclusion

Key Result

Theorem 1

Let $X$ be continuous non-negative random variable having Shannon's entropy $H(X)$ in (shannon), then

Theorems & Definitions (12)

  • Definition 1
  • Example 1
  • Theorem 1
  • Remark 1
  • Definition 2
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6
  • ...and 2 more