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Bayesian estimation for Dagum distribution based on progressive type I interval censoring.

Refah Alotaibi1, Hoda Rezk2, Sanku Dey3

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Summary
This summary is machine-generated.

This study introduces improved estimation methods for the Dagum distribution using progressively censored data. Bayes estimation under squared error loss functions demonstrates superior performance over maximum likelihood estimation.

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Survival Analysis

Background:

  • The Dagum distribution is versatile for modeling various failure rates and aging patterns.
  • Progressively type-I interval censoring is a common data collection method in reliability studies.
  • Accurate parameter estimation is crucial for understanding system reliability and lifespan.

Purpose of the Study:

  • To develop and compare Maximum Likelihood Estimators (MLEs) and Bayesian estimators for the Dagum distribution parameters under progressively type-I interval censoring.
  • To evaluate the performance of different loss functions (Squared Error Loss - SEL, Balanced Squared Error Loss - BSEL) and prior distributions (informative gamma, non-informative uniform).
  • To obtain Bayes predictive estimates and intervals for future observations.

Main Methods:

  • Derivation of Maximum Likelihood Estimators (MLEs) and approximate confidence intervals.
  • Development of Bayesian estimators using SEL and BSEL functions with independent gamma and uniform priors.
  • Monte Carlo simulation study to compare MLEs and Bayesian estimators.
  • Computation of credible intervals and Bayes probability intervals.
  • Obtaining Bayes predictive estimates and intervals using one- and two-sample schemes.

Main Results:

  • Bayes estimators under SEL and BSEL showed lower bias and Mean Squared Errors (MSEs) compared to MLEs.
  • Credible intervals exhibited smaller lengths than confidence intervals.
  • Informative priors generally led to better predictive estimates than non-informative priors.
  • An optimal censoring scheme was identified.

Conclusions:

  • Bayesian estimation approaches, particularly with SEL and informative priors, offer improved accuracy and precision for Dagum distribution parameter estimation under progressive censoring.
  • The findings provide valuable insights for reliability analysis and decision-making in the presence of censored data.