Objective and subjective prior distributions for the Gompertz distribution

Area of Science:

• Statistics
• Reliability Engineering

Background:

• The Gompertz distribution is widely used in reliability and survival analysis.
• Accurate parameter estimation is crucial for reliable predictions.

Purpose of the Study:

• To compare frequentist and Bayesian estimation methods for Gompertz distribution parameters.
• To evaluate the impact of various prior distributions (objective and subjective) on parameter estimates.
• To assess the performance of different estimation techniques using simulation and real data.

Main Methods:

• Derivation of non-informative priors (Jeffreys, Maximal Data Information Prior).
• Development of a subjective prior incorporating expert knowledge via percentiles and Laplace approximation.
• Implementation of Markov Chain Monte Carlo (MCMC) for Bayesian estimation.
• Performance evaluation using bias, mean-squared error, and coverage probabilities via numerical simulations.

Main Results:

• Bayesian estimates incorporating expert knowledge demonstrated competitive performance.
• Comparison of maximum likelihood estimates and various Bayes estimates revealed differences in bias and mean-squared error.
• The choice of prior distribution significantly influences the posterior estimates.

Conclusions:

• Bayesian methods, especially those utilizing expert elicited priors, offer a robust alternative for Gompertz distribution parameter estimation.
• The study provides a comprehensive comparison of estimation strategies for reliability applications.
• Practical application through real data analysis validates the proposed methodologies.