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

Abstract

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.

Keywords and Phrases:

• Censoring
• kernel estimation
• length-bias
• mean squared error
• Shannon entropy

2010 MSC:

• 94A17
• 62G07

Acknowledgements

The first author wishes to thank Cochin University of Science and Technology, India for the financial assistance. The second and third authors wish to thank the support of the University Grants Commission (UGC), Government of India, under the Special Assistance Programme and the second author would like to thank UGC, New Delhi for the financial support under UGC-SMNRI Project.