Strong uniform consistency of nonparametric estimation for quantile-based entropy function under length-biased sampling

For studies in reliability, biometry, and survival analysis, the length-biased distribution is often well-suited for certain natural sampling plans. In this paper, we study the strong uniform consistency of two nonparametric estimators for the quantile-based Shannon entropy in the context of length-biased data. A simulation study is conducted to examine the behavior of the estimators in finite samples, followed by a comparative analysis with existing estimators. Furthermore, the usefulness of the proposed estimators is evaluated using a real dataset.