Statistical Analysis of Adaptive Progressive Type‐I Competing Risks Data Using the Generalized Power Unit Half‐Logistic Geometric Distribution

We investigate parameter estimation difficulties for the generalized power unit half‐logistic geometric (GPUHLG) distribution, proposing an adaptive progressive Type‐I competing risk design to tackle them. The unknown parameters are estimated via both maximum likelihood and Bayesian methodologies. Assuming that population units experience failure due to two independent causes, each adhering to a GPUHLG distribution, a comprehensive competing risks model is formulated. Parameter estimation under the adaptive progressive Type‐I censoring scheme is carried out using the maximum likelihood method, from which asymptotic confidence intervals are obtained. We also derive Bayesian point estimates and credible intervals through Markov chain Monte Carlo (MCMC) techniques. The effectiveness of the proposed methods is demonstrated through applications to both real and simulated datasets.