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A bivariate inverse Weibull distribution and its application in complementary risks model.

Shuvashree Mondal1, Debasis Kundu1

  • 1Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India.

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|June 16, 2022
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Summary

This study introduces an absolutely continuous bivariate inverse Weibull (ACBIW) distribution for analyzing dependent risks, overcoming limitations of existing models. The ACBIW distribution offers a flexible approach for reliability and survival analysis with non-monotone hazard functions.

Keywords:
EM algorithmGamma-Dirichlet priorMarshall–Olkin bivariate distributionPrimary: 62E15Secondary: 62H10block and basu bivariate distributioncomplementary riskmaximum likelihood estimation

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Survival Analysis

Background:

  • The inverse Weibull distribution is a heavy-tailed model with non-monotone hazard functions.
  • A recently introduced bivariate inverse Weibull (BIW) distribution has a singular component, limiting its use with data lacking ties.

Purpose of the Study:

  • To introduce an absolutely continuous bivariate inverse Weibull (ACBIW) distribution.
  • To address limitations of the BIW distribution by omitting its singular component.
  • To analyze dependent complementary risks data.

Main Methods:

  • Developed the absolutely continuous bivariate inverse Weibull (ACBIW) distribution.
  • Proposed the expectation-maximization algorithm for classical maximum likelihood estimation.
  • Utilized a flexible prior and importance sampling for Bayesian estimation.

Main Results:

  • The ACBIW distribution provides a viable model for dependent complementary risks.
  • The expectation-maximization algorithm effectively estimates parameters in the classical approach.
  • Bayesian methods yield robust estimates and credible intervals.

Conclusions:

  • The ACBIW distribution is a valuable extension for survival analysis.
  • Both classical and Bayesian approaches offer effective inference methods.
  • The model demonstrates practical utility through data set analyses.