A flexible Weibull geometric distribution with characterizations and its parameter estimation

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Lifetime data analysis often requires flexible statistical models.
• Existing distributions may not adequately capture complex failure patterns.
• The Weibull-geometric distribution is a candidate for improved modeling.

Purpose of the Study:

• Introduce a novel, more flexible Weibull-geometric distribution.
• Investigate its comprehensive statistical properties.
• Evaluate various parameter estimation techniques.

Main Methods:

• Derivation of probability density, reliability, and failure rate functions.
• Application of the Expectation-Maximization (EM) algorithm for parameter estimation.
• Bayesian inference using Markov Chain Monte Carlo (MCMC) and importance sampling for credible intervals.
• Development of shrinkage preliminary test estimators using Maximum Likelihood and Bayesian approaches.

Main Results:

• The proposed distribution exhibits enhanced flexibility for lifetime data.
• Bayesian and Maximum Likelihood estimators are compared via simulation.
• The EM algorithm effectively computes asymptotic variances and covariances.
• Highest Posterior Density (HPD) credible intervals are derived.

Conclusions:

• The new Weibull-geometric distribution provides a superior model for lifetime data.
• The study validates the performance of proposed estimation techniques.
• The distribution's practical utility is confirmed through real data analysis.