A flexible Weibull geometric distribution with characterizations and its parameter estimation

The current paper introduces a new version of the Weibull-geometric distribution, which offers a more flexible model for lifetime data. The statistical properties of the proposed distribution-such as the probability density function, reliability and failure rate functions, quantiles, and moments-are discussed. The EM algorithm is used to compute the asymptotic variances and covariances of the parameters. Point estimators of the unknown parameters, under various symmetric and asymmetric loss functions, are obtained using the Bayesian framework and the Markov Chain Monte Carlo (MCMC) technique. Furthermore, using the importance sampling procedure, the highest posterior density (HPD) credible intervals for the parameters are derived. Maximum likelihood and Bayesian estimators are also employed to compute the shrinkage preliminary test estimators. Consequently, a simulation study is conducted to evaluate the performance of all proposed estimation methods. Finally, a real data set is analyzed to demonstrate the effectiveness and flexibility of the new distribution.