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Birnbaum Saunders distribution for imprecise data: statistical properties, estimation methods, and real life

Marwa K Hassan1, Muhammad Aslam2

  • 1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, 11566, Egypt.

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|March 24, 2024
PubMed
Summary

This study introduces the neutrosophic Birnbaum-Saunders distribution, a novel statistical model. It explores parameter estimation and validates its real-world applicability, offering a new tool for statistical analysis.

Keywords:
Bayesian estimationBirnbaum–Saunders distributionMaximum likelihood estimationNeutrosophic statisticsSimulation study

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Area of Science:

  • Statistics
  • Probability Theory
  • Neutrosophic Statistics

Background:

  • Neutrosophic statistics extends classical statistics by incorporating uncertainty.
  • The Birnbaum-Saunders distribution is a well-established model for reliability analysis.

Purpose of the Study:

  • To introduce and define the novel neutrosophic Birnbaum-Saunders distribution.
  • To derive its statistical properties and explore parameter estimation methods.
  • To assess the performance and applicability of the new distribution.

Main Methods:

  • Derivation of statistical properties using Mathematica 13.1.1 and R-Studio.
  • Application of Maximum Likelihood Estimation and Bayesian estimation methods.
  • Monte-Carlo simulation for performance evaluation and comparison.

Main Results:

  • The neutrosophic Birnbaum-Saunders distribution is successfully introduced.
  • Parameter estimation methods are developed and simulated.
  • The new distribution shows potential for real-life applications.

Conclusions:

  • The neutrosophic Birnbaum-Saunders distribution offers a flexible alternative to the classical model.
  • The study demonstrates the utility of neutrosophic statistics in reliability.
  • Further research can explore advanced applications of this distribution.