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Likelihood ratio inference for mean residual life of length-biased random variable

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Abstract

In lifetime data analysis, naturally recorded observations are length-biased data if the probability to select an item is proportional to its length. Based on i.i.d. observations of the true distribution, empirical likelihood (EL) procedure is proposed for the inference on mean residual life (MRL) of naturally recorded item. The limit distribution of the EL based log-likelihood ratio is proved to be the chi-square distribution. Under right censorship, since the EL based log-likelihood ratio leads to a scaled chi-square distribution and estimating the scale parameter leads to lower coverage of confidence interval, we propose an algorithm to calculate the likelihood ratio (LR) directly. The corresponding log-likelihood ratio converges to the standard chi-square distribution and the corresponding confidence interval has a better coverage. Simulation studies are used to support the theoretical results.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Wei Liang

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Jun-shan Shen

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shu-yuan He

Authors
  1. Wei Liang
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  2. Jun-shan Shen
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  3. Shu-yuan He
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Corresponding author

Correspondence to Wei Liang.

Additional information

Supported by the National Natural Science Foundation of China (No. 11171230,11231010,11471272).

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Liang, W., Shen, Js. & He, Sy. Likelihood ratio inference for mean residual life of length-biased random variable. Acta Math. Appl. Sin. Engl. Ser. 32, 269–282 (2016). https://doi.org/10.1007/s10255-016-0562-0

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  • DOI: https://doi.org/10.1007/s10255-016-0562-0

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