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On the existence and uniqueness of the maximum likelihood estimates of parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples

  • Xiaojun ZhuEmail author
  • N. Balakrishnan
  • Helton Saulo
Article
  • 28 Downloads

Abstract

In this paper, we discuss the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of Laplace Birnbaum–Saunders distribution based on Type-I, Type-II and hybrid censored samples. We first derive the relationship between the MLEs of the two parameters and then discuss the monotonicity property of the profile likelihood function. Numerical iterative procedure is then discussed for determining the MLEs of the parameters. Finally, for illustrative purpose, we analyze one real data from the literature and present some graphical illustrations of the approach.

Keywords

Birnbaum–Saunders distribution Existence Generalized Birnbaum–Saunders distribution Hybrid censoring Laplace Birnbaum–Saunders distribution Maximum likelihood estimate Type-I censoring Type-II censoring Uniqueness 

Mathematics Subject Classification

62N01 62N02 65C60 

Notes

Acknowledgements

We express our sincere thanks to the anonymous reviewers for their useful comments and suggestion on an earlier version of this manuscript which led to this improved version.

Funding

This research was supported by the National Natural Science Foundation of China—Young Scientists Fund [No. 11801459], Jiangsu Science and Technology Programme—The Young-Scholar Programme [No. BK20180241] and the Research Development Fund of Xian-Jiaotong Liverpool University [No. RDF-17-01-20]. The second author thanks the Natural Sciences and Engineering Research Council of Canada for supporting this research.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesXi’an Jiaotong-Liverpool UniversitySuzhouPeople’s Republic of China
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  3. 3.Department of StatisticsUniversity of BrasiliaBrasíliaBrazil

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