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Reliability estimation in Lindley distribution with progressively type II right censored sample

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  • Krishna, Hare
  • Kumar, Kapil

Abstract

In this paper we discuss one parameter Lindley distribution. It is suggested that it may serve as a useful reliability model. The model properties and reliability measures are derived and studied in detail. For the estimation purposes of the parameter and other reliability characteristics maximum likelihood and Bayes approaches are used. Interval estimation and coverage probability for the parameter are obtained based on maximum likelihood estimation. Monte Carlo simulation study is conducted to compare the performance of the various estimates developed. In view of cost and time constraints, progressively Type II censored sample data are used in estimation. A real data example is given for illustration.

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  • Krishna, Hare & Kumar, Kapil, 2011. "Reliability estimation in Lindley distribution with progressively type II right censored sample," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 281-294.
    • Handle: RePEc:eee:matcom:v:82:y:2011:i:2:p:281-294
    DOI: 10.1016/j.matcom.2011.07.005
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    1. Biswabrata Pradhan & Debasis Kundu, 2009. "On progressively censored generalized exponential distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 497-515, November.
    2. Ghitany, M.E. & Atieh, B. & Nadarajah, S., 2008. "Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 78(4), pages 493-506.
    3. Basak, Prasanta & Basak, Indrani & Balakrishnan, N., 2009. "Estimation for the three-parameter lognormal distribution based on progressively censored data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3580-3592, August.
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    Cited by:

    1. Vikas Kumar Sharma & Sanjay Kumar Singh & Umesh Singh & Khair Ul-Farhat, 2017. "Bayesian estimation on interval censored Lindley distribution using Lindley’s approximation," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 799-810, November.
    2. Kapil Kumar & Renu Garg & Hare Krishna, 2017. "Nakagami distribution as a reliability model under progressive censoring," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(1), pages 109-122, March.
    3. Singh, Bhupendra & Gupta, Puneet Kumar, 2012. "Load-sharing system model and its application to the real data set," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(9), pages 1615-1629.
    4. E.I., Abdul Sathar & K.V., Viswakala, 2019. "Non-parametric estimation of Kullback–Leibler discrimination information based on censored data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    5. A. Asgharzadeh & A. Fallah & M. Z. Raqab & R. Valiollahi, 2018. "Statistical inference based on Lindley record data," Statistical Papers, Springer, vol. 59(2), pages 759-779, June.
    6. K. Muralidharan & Pratima Bavagosai, 2023. "Instantaneous failure analysis on Lindley distribution under progressive type II censoring," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(4), pages 1312-1339, August.
    7. Sanku Dey & Vikas Kumar Sharma & M. Z. Anis & Babita Yadav, 2017. "Assessing lifetime performance index of Weibull distributed products using progressive type II right censored samples," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 318-333, June.
    8. Iman Makhdoom & Parviz Nasiri & Abbas Pak, 2016. "Bayesian approach for the reliability parameter of power Lindley distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 7(3), pages 341-355, September.
    9. Neha Goel & Hare Krishna, 2022. "Estimation in Residual lifetime Lindley distribution with Type II censored data," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 363-374, February.
    10. Valiollahi, R. & Raqab, Mohammad Z. & Asgharzadeh, A. & Alqallaf, F.A., 2018. "Estimation and prediction for power Lindley distribution under progressively type II right censored samples," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 32-47.
    11. Saadati Nik, A. & Asgharzadeh, A. & Raqab, Mohammad Z., 2021. "Estimation and prediction for a new Pareto-type distribution under progressive type-II censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 508-530.
    12. Muhammad Aslam Mohd Safari & Nurulkamal Masseran & Muhammad Hilmi Abdul Majid, 2020. "Robust Reliability Estimation for Lindley Distribution—A Probability Integral Transform Statistical Approach," Mathematics, MDPI, vol. 8(9), pages 1-21, September.

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