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Inference for partially observed competing risks model for Kumaraswamy distribution under generalized progressive

Amulya Kumar Mahto1, Chandrakant Lodhi2, Yogesh Mani Tripathi1

  • 1Department of Mathematics, Indian Institute of Technology, Patna, India.

Journal of Applied Statistics
|June 27, 2022
PubMed
Summary

This study introduces a competing risks model using the Kumaraswamy distribution under generalized progressive hybrid censoring. It establishes parameter estimation methods and evaluates their performance through simulations for reliability analysis.

Keywords:
Bayes estimateCompeting risksFisher information matrixmaximum likelihood estimateorder restriction

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Survival Analysis

Background:

  • Competing risks models are crucial for analyzing multiple failure causes.
  • The Kumaraswamy distribution offers flexibility for modeling lifetime data.
  • Generalized progressive hybrid censoring is an efficient data collection scheme.

Purpose of the Study:

  • To develop statistical inference methods for a competing risks model with Kumaraswamy latent failure times.
  • To address challenges posed by partially observed failure causes and censoring.
  • To investigate the impact of order-restricted shape parameters on inference.

Main Methods:

  • Establishing the existence and uniqueness of Maximum Likelihood Estimators (MLEs).
  • Utilizing asymptotic distribution theory for confidence interval construction.
  • Computing Bayesian estimators and credible intervals.
  • Employing Monte Carlo simulations to assess estimator performance.

Main Results:

  • The existence and uniqueness of MLEs for model parameters are proven.
  • Asymptotic confidence intervals are derived.
  • Bayesian estimation provides credible intervals for parameters.
  • Simulations demonstrate the performance of various estimation techniques.

Conclusions:

  • The proposed methods provide valid statistical inference for the studied competing risks model.
  • The findings are illustrated with a real-world data analysis.
  • The study contributes to the statistical analysis of complex failure data.