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Classical and Bayesian Inference of Conditional Stress-Strength Model under Kumaraswamy Distribution.

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  • 1Department of Mathematics, College of Science, Jouf University, Sakaka, Saudi Arabia.

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This study introduces conditional stress-strength models for the Kumaraswamy distribution. Researchers derived the maximum likelihood estimator and its confidence intervals, alongside Bayesian and bootstrap estimations.

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Area of Science:

  • Statistics
  • Probability Theory
  • Reliability Engineering

Background:

  • Stress-strength models are crucial for system reliability.
  • Conditional stress-strength models offer a more nuanced analysis.
  • The Kumaraswamy distribution is a flexible probability model.

Purpose of the Study:

  • To extend stress-strength models to a conditional framework.
  • To analyze the Kumaraswamy distribution within this conditional model.
  • To provide statistical estimation and inference methods.

Main Methods:

  • Maximum Likelihood Estimation (MLE) for model parameters.
  • Asymptotic distribution theory for the MLE.
  • Construction of confidence intervals.
  • Bayesian estimation techniques.
  • Bootstrap resampling methods.

Main Results:

  • The maximum likelihood estimator for the conditional stress-strength model was derived.
  • The asymptotic distribution of the estimator was determined.
  • Confidence intervals for the estimator were established.
  • Bayesian and bootstrap estimates were computed.

Conclusions:

  • The study successfully developed and analyzed a conditional stress-strength model for the Kumaraswamy distribution.
  • Various estimation techniques (MLE, Bayesian, bootstrap) were applied and evaluated.
  • The findings contribute to reliability analysis and statistical modeling.