A Nonparametric Estimator of Bivariate Quantile Residual Life Model with Application to Tumor Recurrence Data Set

  • M. KayidEmail author
  • M. Shafaei Noughabi
  • A. M. Abouammoh


Recently, Shafaei and Kayid (Statistical Papers, 2017) introduced and studied the bivariate quantile residual life model. It has been shown that two suitable bivariate quantile residual life functions characterize the underlying distribution uniquely. In the current investigation, we first propose a nonparametric estimator of this new model. The estimator is strongly consistent and, on proper normalization, asymptotically follows a bivariate Gaussian process. An extensive simulation study has been conducted to discuss the behavior of the estimator. Finally, to illustrate the applications, a real data set related to a tumor recurrence trial is presented and discussed.


Partial empirical quantile process Bivariate empirical survival process Weak convergence Bivariate normal distribution 

Mathematics Subject Classification

60E15 62N05 



We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. The support of University of Gonabad under grant No. 94-16 is gratefully acknowledged. The project of first and third authors was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center.

Funding Information

This study received support from the University of Gonabad under grant no. 94-16 and King Saud University, Deanship of Scientific Research, College of Science Research Center.


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Copyright information

© The Classification Society 2018

Authors and Affiliations

  • M. Kayid
    • 1
    • 2
    Email author
  • M. Shafaei Noughabi
    • 3
  • A. M. Abouammoh
    • 1
  1. 1.Department of Statistics and Operations Research, College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  2. 2.Department of Mathematics and Computer Science, Faculty of ScienceSuez UniversitySuezEgypt
  3. 3.Department of Mathematics and StatisticsUniversity of GonabadGonabadIran

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