Inference of dynamic weighted cumulative residual entropy for Burr XII distribution based on progressive censoring

The dynamic weighted cumulative residual (DWCR) entropy is regarded as an additional measure of uncertainty related to the residual lifetime function in several disciplines, including survival analysis and reliability. This article presents the DWCR formula based on Havarda and Charvat. This measurement is called the DWCR Havarda and Charvat entropy (DWCRHCE). This work uses progressive Type II censoring to investigate the implications of DWCR Tsallis entropy (DWCRTE), DWCR Rényi entropy (DWCRRE), and DWCRHCE for the Burr XII distribution. Both classical and Bayesian methods are used to derive the estimators of these entropy metrics. Assuming independent gamma priors, we get the Bayes estimator of the suggested measures. Due to the lack of explicit forms, the MetropolisHastings approach was offered to determine the Bayes estimates for symmetric and asymmetric loss functions. To determine the efficacy of the suggested estimating techniques, several simulations were run for different censoring schemes. The simulation analysis leads us to the conclusion that, under a precautionary loss function followed by a linear exponential loss function, the Bayesian estimates of DWCRTE are generally more effective than the DWCRHCE or DWCRRE. Compared to maximum likelihood estimates, Bayesian estimates are preferred for different metrics. After that, a detailed explanation of the process is provided by looking at real data. The analysis of real-world data, specifically the Shasta reservoir water capacity data, aligns with the findings from simulated data. Notably, these findings have crucial implications for effective water resource management decisions.