Simulation Study for Estimating the Parameters and Reliability Function of Weighted Exponential Distribution with Fuzzy Data

Authors

  • Lamyaa Khalid Hussein Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadiriya, Baghdad, Iraq.
  • Nadia Hashim Al-Noor Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.

DOI:

https://doi.org/10.22401/93562w90

Keywords:

Weighted Exponential Distribution , Maximum Likelihood Estimation , Bayesian Estimation , Newton-Raphson Algorithm , Lindley approximation , Fuzzy Data

Abstract

This paper investigates the estimation of the two unknown parameters and the reliability function of the weighted exponential distribution. It explores Bayesian and non-Bayesian (maximum likelihood) estimation methods when the information available is in the form of fuzzy data. The Newton-Raphson algorithm is used to obtain the maximum likelihood estimates. In Bayes estimation, the symmetric squared error loss function is used. This loss function links equal importance to the losses due to overestimating and underestimating equal magnitude. Lindley approximation procedure in Bayesian estimation theory is used to evaluate the ratio of integrals. A comparative analysis using simulation is carried out to evaluate the performance of the obtained parameters estimators using mean squared error criteria and the performance of the obtained reliability estimators using integrated mean squared error criteria. The simulation results demonstrate that, for different sample sizes, the performance of Bayes estimates surpasses the maximum likelihood, and that all estimators perform consistently.

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Published

2024-06-15

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How to Cite

(1)
Simulation Study for Estimating the Parameters and Reliability Function of Weighted Exponential Distribution With Fuzzy Data. ANJS 2024, 27 (2), 145-154. https://doi.org/10.22401/93562w90.

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