IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v18y2017i2p291-310n3.html
   My bibliography  Save this article

A Three-Parameter Weighted Lindley Distribution and its Applications to Model Survival Time

Author

Listed:
  • Shanker Rama

    (Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea)

  • Shukla Kamlesh Kumar

    (Department of Statistics, Eritrea Institute of Technology, Asmara, Eritrea)

  • Mishra Amarendra

    (Department of Statistics, Patna University, Patna, India)

Abstract

In this paper a three-parameter weighted Lindley distribution, including Lindley distribution introduced by Lindley (1958), a two-parameter gamma distribution, a two-parameter weighted Lindley distribution introduced by Ghitany et al. (2011) and exponential distribution as special cases, has been suggested for modelling lifetime data from engineering and biomedical sciences. The structural properties of the distribution including moments, coefficient of variation, skewness, kurtosis and index of dispersion have been derived and discussed. The reliability properties, including hazard rate function and mean residual life function, have been discussed. The estimation of its parameters has been discussed using the maximum likelihood method and the applications of the distribution have been explained through some survival time data of a group of patients suffering from head and neck cancer, and the fit has been compared with a one-parameter Lindley distribution and a two-parameter weighted Lindley distribution.

Suggested Citation

  • 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, Statistics Poland, vol. 18(2), pages 291-310, June.
    • Handle: RePEc:vrs:stintr:v:18:y:2017:i:2:p:291-310:n:3
    DOI: 10.21307/stattrans-2016-071
    as

    Download full text from publisher

    File URL: https://doi.org/10.21307/stattrans-2016-071
    Download Restriction: no
    File URL: https://libkey.io/10.21307/stattrans-2016-071?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Rama Shanker, 2016. "Sujatha Distribution And Its Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 391-410, September.
    10. 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.
    11. 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.
    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.
    13. Shanker R & Kamlesh KK & Fesshaye H, 2017. "A Two Parameter Lindley Distribution: Its Properties and Applications," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 1(4), pages 85-90, May.
    14. R. Shanker, 2016. "Sujatha Distribution and its Applications," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(3), pages 391-410, September.
    15. 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.
    16. 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.
    17. Shanker Rama, 2016. "Sujatha Distribution and its Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 391-410, September.
    18. Friday Ikechukwu Agu & Joseph Thomas Eghwerido, 2021. "Agu-Eghwerido distribution, regression model and applications," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 59-76, December.
    19. Hurairah Ahmed & Alabid Abdelhakim, 2020. "Beta transmuted Lomax distribution with applications," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 13-34, June.
    20. Tzong-Ru Tsai & Yuhlong Lio & Jyun-You Chiang & Yi-Jia Huang, 2022. "A New Process Performance Index for the Weibull Distribution with a Type-I Hybrid Censoring Scheme," Mathematics, MDPI, vol. 10(21), pages 1-17, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:stintr:v:18:y:2017:i:2:p:291-310:n:3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://stat.gov.pl/en/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.