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A Robust Bayesian Study on Two-Parameter Exponential Distribution

Author

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  • Muhammad Aamir
  • Sulaiman Khan
  • Fayaz Ahmad
  • Muhammad Naeem
  • Muhammad Arif
  • Mukhtaj Khan
  • Abdul Qadeer Khan

Abstract

In this study, the two-parameter exponential distribution is studied under a robust Bayesian approach. This distribution has a wide range of applications in all most every field of science. Posterior distribution of scale parameter is derived assuming different noninformative (Uniform and Jeffrey’s) and informative (Inverted Gamma, Gumbel Type-II, and Inverse Levy’s) priors. Elicitations of the hyper-parameters are done using the prior predictive distribution based on the expert predictive probabilities. Expressions of Bayes estimators (BEs) and Bayes posterior risks (BPRs) are derived under squared error loss function (SELF), precautionary loss function (PLF), quadratic loss function (QLF), and weighted loss function. The behaviours of posterior distributions of the parameter are shown through graphs. The hypotheses have also been tested for the parameters. It is found that Gumbel Type-II prior and QLF perform better for the analysis of scale parameters.

Suggested Citation

  • Muhammad Aamir & Sulaiman Khan & Fayaz Ahmad & Muhammad Naeem & Muhammad Arif & Mukhtaj Khan & Abdul Qadeer Khan, 2023. "A Robust Bayesian Study on Two-Parameter Exponential Distribution," Mathematical Problems in Engineering, Hindawi, vol. 2023, pages 1-15, April.
    • Handle: RePEc:hin:jnlmpe:2281813
    DOI: 10.1155/2023/2281813
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