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Length-biased data appear when sampling lifetimes by cross-section. This article presents a nonparametric kernel estimators of entropy function for the length-biased sample under type I censoring. We have shown that the proposed estimator is consistent and asymptotically normal under suitable regularity conditions. We have conducted simulation studies to assess the performance of the proposed estimators.

Estimation of Shannon Entropy in the Presence of Length-Bias and Type I Censoring