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A two-parameter weighted Lindley distribution and its applications to survival data

Author

Listed:
  • Ghitany, M.E.
  • Alqallaf, F.
  • Al-Mutairi, D.K.
  • Husain, H.A.

Abstract

A two-parameter weighted Lindley distribution is proposed for modeling survival data. The proposed distribution has the property that the hazard rate (mean residual life) function exhibits bathtub (upside-down bathtub) or increasing (decreasing) shapes. Simulation studies are conducted to investigate the performance of the maximum likelihood estimators and the asymptotic confidence intervals of the parameters. Applications of the proposed model to real survival data are presented.

Suggested Citation

  • Ghitany, M.E. & Alqallaf, F. & Al-Mutairi, D.K. & Husain, H.A., 2011. "A two-parameter weighted Lindley distribution and its applications to survival data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1190-1201.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:6:p:1190-1201
    DOI: 10.1016/j.matcom.2010.11.005
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    References listed on IDEAS

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    1. M. E. Ghitany & D. K. Al-Mutairi, 2008. "Size-biased Poisson-Lindley distribution and its application," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 299-311.
    2. Ghitany, M.E. & Al-Mutairi, D.K. & Nadarajah, S., 2008. "Zero-truncated Poisson–Lindley distribution and its application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 279-287.
    3. 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.
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    Cited by:

    1. Sanku Dey & Indranil Ghosh & Devendra Kumar, 2019. "Alpha-Power Transformed Lindley Distribution: Properties and Associated Inference with Application to Earthquake Data," Annals of Data Science, Springer, vol. 6(4), pages 623-650, December.
    2. Shikhar Tyagi & Arvind Pandey & Christophe Chesneau, 2022. "Weighted Lindley Shared Regression Model for Bivariate Left Censored Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 655-682, November.
    3. Mojtaba Alizadeh & Seyyed Fazel Bagheri & Mohammad Alizadeh & Saralees Nadarajah, 2017. "A new four-parameter lifetime distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 767-797, April.
    4. Rama Shanker & Kamlesh Kumar Shukla & Amarendra Mishra, 2017. "A Three-Parameter Weighted Lindley Distribution And Its Applications To Model Survival Time," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 291-310, June.
    5. 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.
    6. Deepesh Bhati & Mohd. Malik & H. Vaman, 2015. "Lindley–Exponential distribution: properties and applications," METRON, Springer;Sapienza Università di Roma, vol. 73(3), pages 335-357, December.
    7. A. Shabani & M. Khaleghi Moghadam & A. Gholami & E. Moradi, 2018. "Exponentiated Power Lindley Logarithmic: Model, Properties and Applications," Annals of Data Science, Springer, vol. 5(4), pages 583-613, December.
    8. Bhupendra Singh & Neha Choudhary, 2017. "The exponentiated Perks 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. 8(2), pages 468-478, June.
    9. Morad Alizadeh & Ahmed Z. Afify & M. S. Eliwa & Sajid Ali, 2020. "The odd log-logistic Lindley-G family of distributions: properties, Bayesian and non-Bayesian estimation with applications," Computational Statistics, Springer, vol. 35(1), pages 281-308, March.
    10. Francisco Louzada & Pedro Luiz Ramos, 2017. "A New Long-Term Survival Distribution," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 1(5), pages 104-109, May.
    11. Mario A. Rojas & Yuri A. Iriarte, 2022. "A Lindley-Type Distribution for Modeling High-Kurtosis Data," Mathematics, MDPI, vol. 10(13), pages 1-19, June.
    12. Devendra Kumar & Anju Goyal, 2019. "Order Statistics from the Power Lindley Distribution and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(1), pages 153-177, March.
    13. Duha Hamed & Ahmad Alzaghal, 2021. "New class of Lindley distributions: properties and applications," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-22, December.
    14. Alex Mota & Eder A. Milani & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Oilson G. Junior & Vera L. D. Tomazella & Francisco Louzada, 2023. "A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 883-909, September.
    15. Cesar Augusto Taconeli & Suely Ruiz Giolo, 2020. "Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data," Computational Statistics, Springer, vol. 35(4), pages 1827-1851, December.
    16. Alex Mota & Eder A. Milani & Vinicius F. Calsavara & Vera L. D. Tomazella & Jeremias Leão & Pedro L. Ramos & Paulo H. Ferreira & Francisco Louzada, 2021. "Weighted Lindley frailty model: estimation and application to lung cancer data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 561-587, October.
    17. Shanker Rama & Shukla Kamlesh Kumar & Mishra Amarendra, 2017. "A Three-Parameter Weighted Lindley Distribution and its Applications to Model Survival Time," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 291-310, June.
    18. Ali Doostmoradi, 2018. "A New Distribution with two parameters to Lifetime Data," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 8(2), pages 30-35, September.
    19. Showkat Ahmad Dar & Anwar Hassan & Ahmad Para Bilal & Sameer Ahmad Wani, 2021. "A new count data model applied in the analysis of vaccine adverse events and insurance claims," Statistics in Transition New Series, Polish Statistical Association, vol. 22(3), pages 157-174, September.
    20. Marcelo Bourguignon, 2019. "An Alternative Conjugate Prior Distribution for Positive Parameters," Annals of Data Science, Springer, vol. 6(2), pages 237-243, June.
    21. Devendra Kumar & Anju Goyal, 2019. "Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application," Annals of Data Science, Springer, vol. 6(4), pages 707-736, December.
    22. A. Mishra & R. Shanker, 2013. "A two-parameter Lindley distribution," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 14(1), pages 45-56, March.

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