Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2023, Vol. 40 ›› Issue (6): 1001-1010.doi: 10.3969/j.issn.1005-3085.2023.06.011

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Moment-type Estimations of Mean Residual Life Function with Complete Length-biased Data

WU Hongping   

  1. School of Big Data and Fundamental Sciences, Shandong Institute of Petroleum and Chemical Technology, Dongying 257061
  • Received:2021-04-13 Accepted:2022-04-29 Online:2023-12-15 Published:2024-02-15
  • Supported by:
    The National Social Science Foundation of China (20TJ060); the Science Development Fund of Dongying (DJ2021023).

Abstract:

Length-biased data widely exist in life research. However, there are relatively few studies on the mean residual life under complete length-biased data. As one of the important indicators to evaluate individuals’survival, mean residual life attracts more and more attention from statistical researchers. In order to construct nonparametric estimations of the mean residual life function under complete length-biased data, two estimations are derived by utilizing the idea of moment estimation. It is proved that the proposed estimations converge in distribution to two zero-mean normal variables under moderate conditions, respectively. In order to evaluate the performance of the proposed estimators in finite samples, a series of numerical simulations are carried out, and the simulation results are compared with those of existing methods. The numerical results show the rationality of two proposed estimations.

Key words: residual life, mean, length-biased data, moment-type estimation, central limit theorem

CLC Number: