🤖 AI Summary
This study addresses the survival dynamics of zebra finches under varying food availability by developing a lifetime inference model incorporating two competing causes of failure. Assuming lifetimes follow a Gompertz distribution, the authors propose an improved adaptive Type-II progressive censoring scheme and estimate model parameters using both maximum likelihood and Bayesian approaches—employing non-informative and informative priors—along with several loss functions to construct highest posterior density (HPD) credible intervals. Theoretical analysis establishes the unique existence of the parameter estimates, while Monte Carlo simulations evaluate and compare estimation performance. The methodology is further validated using real avian data. Additionally, three optimality criteria for censoring schemes are introduced, offering novel guidance for designing survival experiments.
📝 Abstract
This paper studies survival of certain bird species (Zebra Finches) under different food availability conditions. A competing risks model is studied under improved adaptive type-II progressive censoring scheme (IAT-II PCS) referring to this phenomena. Two independent competing causes of failure are considered where lifetime of these failures are assumed to follow Gompertz distribution with unknown scale and shape parameters. Maximum likelihood estimators (MLEs) of the unknown parameters are derived. It is established that they exist uniquely. Asymptotic confidence intervals (ACIs) are also constructed using asymptotic normality property of the MLE. Bayes estimates are obtained with respect to both non-informative and informative priors under different loss functions. Highest posterior density (HPD) credible intervals are calculated. A Monte Carlo simulation study is conducted to compare the performance of the proposed estimates. Three optimality criteria are studied to obtain the optimal censoring scheme. Finally, a real life data set is analyzed for further illustrations.