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Vague data analysis using neutrosophic Jarque-Bera test.

Muhammad Aslam1, Rehan Ahmad Khan Sherwani2, Muhammad Saleem3

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Summary
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This study introduces a modified Jarque-Bera test for interval-valued data, enhancing normality assessment in neutrosophic environments. The new test effectively handles uncertainty, outperforming the existing method with real-world gold mine data.

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Area of Science:

  • Statistics
  • Decision Science
  • Data Analysis

Background:

  • Parametric tests are widely used in decision-making but often require normality assumptions.
  • The Jarque-Bera test assesses normality but is limited to exact data, excluding interval-valued or neutrosophic data.
  • Interval-valued data, common in fuzzy or indeterminate situations, poses challenges for standard statistical tests.

Purpose of the Study:

  • To modify the existing Jarque-Bera test statistic to accommodate interval-valued data.
  • To develop a new Jarque-Bera test operational procedure for data under a neutrosophic environment.
  • To assess the effectiveness of the proposed neutrosophic Jarque-Bera test for normality validation.

Main Methods:

  • Modification of the Jarque-Bera test statistic for interval-valued data.
  • Development of a new operational procedure for the modified test within a neutrosophic framework.
  • Application and comparison of the proposed test with the existing Jarque-Bera test using real gold mine data.

Main Results:

  • The modified Jarque-Bera test successfully handles interval-valued data in a neutrosophic environment.
  • The proposed neutrosophic Jarque-Bera test demonstrates effectiveness and informativeness for data with indeterminacy.
  • Comparison with the existing test using real gold mine data confirmed the suitability of the new approach.

Conclusions:

  • The newly proposed neutrosophic Jarque-Bera test is a valuable tool for normality assessment with interval-valued data.
  • The modified test extends the applicability of the Jarque-Bera test to situations involving uncertainty and fuzzy logic.
  • The findings suggest the neutrosophic Jarque-Bera test is more suitable than the existing test for data under indeterminacy.