Skip to main content
SpringerLink
Log in

Bayesian estimation on interval censored Lindley distribution using Lindley’s approximation

  • Original Article
  • Published:
International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

Interval censored data commonly arise in engineering and biomedical sciences. The present study deals with Bayesian estimation of interval censored lifetime data while it is assumed that lifetimes follow Lindley distribution. Assuming Jeffrey’s and gamma prior distributions, Bayes estimator of the Lindley parameter has been constructed under symmetric, squared error loss and asymmetric, general entropy loss functions. In addition, Bayes estimators for mean life, reliability and hazard rate have also been constructed. Since posterior distribution can not be reduced to any standard distribution, Lindley’s approximation technique has been utilized for Bayesian computations. The performances of the Bayes estimators has been compared with corresponding maximum likelihood estimators on the basis of simulated samples. Real data sets from engineering and biomedical fields have been analysed for illustration purposes .

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Al-Mutairi DK, Ghitany ME, Kundu D (2013) Inferences on stress-strength reliability from lindley distributions. Commun Stat Theory Methods 42:1443–1463

    Article  MATH  MathSciNet  Google Scholar 

  • Ali S, Aslam M, Kazmi SMA (2013) A study of the effect of the loss function on bayes estimate, posterior risk and hazard function for lindley distribution. Appl Math Model 37:6068–6078

    Article  MATH  MathSciNet  Google Scholar 

  • Bansal AK (2007) Bayesian parametric inference. Narosa, Delhi

    Google Scholar 

  • Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, New York

    Book  MATH  Google Scholar 

  • Calabria R, Pulcini G (1996) Point estimation under asymmetric loss functions for left-truncated exponential samples. Commun Stat Theory Meth 25:585–600

    Article  MATH  MathSciNet  Google Scholar 

  • Courgeau D, Najim J (1996) Population: an english selection. volume 8. chapter Interval-censored event history analysis, pp 191–298

  • Deshpande JV (2005) Life time data: statistical models and methods, vol 11. World Scientific Publishing Co. Pte. Ltd, Singapore

    MATH  Google Scholar 

  • Dube M, Garg R, Krishna H (2015) On progressively first failure censored lindley distribution. Comput Stat. doi:10.1007/s00180-015-0622-6

    MATH  Google Scholar 

  • Ghitany ME, Atieh B, Nadarajah S (2007) Lindley distribution and its application. Math Comput Simul 78:439–506

    MATH  MathSciNet  Google Scholar 

  • Gupta PK, Singh B (2013) Parameter estimation of lindley distribution with hybrid censored data. Int J Syst Assur Eng Manag 4:378–385

    Article  Google Scholar 

  • Guure CB, Dwomoh NAID, Bosomprah S (2014) Bayesian statistical inference of the loglogistic model with interval-censored lifetime data. Math Compute Simul

  • Jeffrey H (2003) Theory of probability. Oxford University Press, Oxford

    Google Scholar 

  • Jianguo S (2006) The statistical analysis of interval-censored failure time data. Springer, New York

    MATH  Google Scholar 

  • Krishna H, Kumar K (2011) Reliability estimation in lindley distribution with progressively type-II right censored sample. Math Comput Simul 82:281–294

    Article  MATH  MathSciNet  Google Scholar 

  • Kumar K, Krishna H, Garg R (2014) Estimation of \(p(y<x)\) in lindley distribution using progressively first failure censoring. Int J Syst Assur Eng Manag, pp 1–12

  • JF Lawless (2003) Statistical models and methods for lifetime data. Wiley, New York

    Google Scholar 

  • Lee ET, Wang JW (2003) Statistical methods for survival data analysis. Wiley, Hoboken

    Book  MATH  Google Scholar 

  • Lindley D (1980) Approximate bayesian methods. Trabajos de Estadistica 31:223–237

    Article  MATH  MathSciNet  Google Scholar 

  • Lindley DV (1958) Fiducial distributions and bayes theorem. J R Stat Soc 20:102–107

    MATH  MathSciNet  Google Scholar 

  • Lindsey JC, Ryan LM (1998) Tutorial in biostatistics methods for interval-censored data. Stat Med 17:219–238

    Article  Google Scholar 

  • Mazucheli J, Achcar JA (2011) A two-parameter lindley distribution for modeling waiting and survival times data. Comput Methods Programs Biomed 104:188–192

    Article  Google Scholar 

  • Peto R (1973) Experimental survival curves for interval-censored data. J R Stat Soc 22:86–91

    Google Scholar 

  • Schworer A, Hovey DP (2004) Newton–Raphson versus fisher scoring algorithms in calculating maximum likelihood estimates. Electronic proceedings of undergraduate Mathematics Day, University of Dayton, OH, USA, vol 1, pp 1–11

  • Sharma VK, Singh SK, Singh U, Agiwal V (2015) The inverse lindley distribution: a stress reliability model with application to head and neck cancer data. J Ind Prod Eng 32:162–173

    Google Scholar 

  • Singh B, Gupta PK (2012) Load-sharing system model and its application to the real data set. Math Comput Simul 82:1615–1629

    Article  MATH  MathSciNet  Google Scholar 

  • Singh PK, Singh SK, Singh U (2008) Bayes estimator of inverse gaussian parameters under general entropy loss function using lindleys approximation. Commun Stat Simul Comput 37:1750–1762

    Article  MATH  MathSciNet  Google Scholar 

  • Turnbull BW (1976) The emperical distribution with arbitrarily grouped censored and truncated data. J R Stat Soc 38:290–295

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Institute of Infrastructure Technology, Research and Management (IITRAM), Maninagar East, Ahmedabad, India

    Vikas Kumar Sharma

  2. Department of Statistics, Central University of Rajasthan, Bandersindri, Ajmer, India

    Vikas Kumar Sharma & Khair Ul-Farhat

  3. Department of Statistics and DST-CIMS, Banaras Hindu University, Varanasi, India

    Sanjay Kumar Singh & Umesh Singh

Authors
  1. Vikas Kumar Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sanjay Kumar Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Umesh Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Khair Ul-Farhat
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vikas Kumar Sharma.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sharma, V.K., Singh, S.K., Singh, U. et al. Bayesian estimation on interval censored Lindley distribution using Lindley’s approximation. Int J Syst Assur Eng Manag 8 (Suppl 2), 799–810 (2017). https://doi.org/10.1007/s13198-016-0528-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13198-016-0528-x

Keywords

Search

Navigation