IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2146-d454753.html
   My bibliography  Save this article

A New Family of Extended Lindley Models: Properties, Estimation and Applications

Author

Listed:
  • Abdulrahman Abouammoh

    (Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia)

  • Mohamed Kayid

    (Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
    Department of Mathematics and Computer Science, Faculty of Science, Suez University, Suez 43511, Egypt)

Abstract

There are many proposed life models in the literature, based on Lindley distribution. In this paper, a unified approach is used to derive a general form for these life models. The present generalization greatly simplifies the derivation of new life distributions and significantly increases the number of lifetime models available for testing and fitting life data sets for biological, engineering, and other fields of life. Several distributions based on the disparity of the underlying weights of Lindley are shown to be special cases of these forms. Some basic statistical properties and reliability functions are derived for the general forms. In addition, comparisons among various forms are investigated. Moreover, the power distribution of this generalization has also been considered. Maximum likelihood estimator for complete and right-censored data has been discussed and in simulation studies, the efficiency and behavior of it have been investigated. Finally, the proposed models have been fit to some data sets.

Suggested Citation

  • Abdulrahman Abouammoh & Mohamed Kayid, 2020. "A New Family of Extended Lindley Models: Properties, Estimation and Applications," Mathematics, MDPI, vol. 8(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2146-:d:454753
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2146/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2146/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Richard L. Smith & J. C. Naylor, 1987. "A Comparison of Maximum Likelihood and Bayesian Estimators for the Three‐Parameter Weibull Distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 358-369, November.
    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.
    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. 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.
    2. Rama Shanker, 2016. "Sujatha Distribution And Its Applications," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 391-410, September.
    3. R. Shanker, 2016. "Sujatha Distribution and its Applications," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(3), pages 391-410, September.
    4. Shanker Rama, 2016. "Sujatha Distribution and its Applications," Statistics in Transition New Series, Statistics Poland, vol. 17(3), pages 391-410, September.
    5. Hurairah Ahmed & Alabid Abdelhakim, 2020. "Beta transmuted Lomax distribution with applications," Statistics in Transition New Series, Statistics Poland, vol. 21(2), pages 13-34, June.
    6. 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.
    7. Cha, Ji Hwan, 2019. "Poisson Lindley process and its main properties," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 74-81.
    8. Irshad M. R. & Maya R., 2018. "On A Less Cumbersome Method Of Estimation Of Parameters Of Lindley Distribution By Order Statistics," Statistics in Transition New Series, Statistics Poland, vol. 19(4), pages 597-620, December.
    9. 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.
    10. Yaoting Yang & Weizhong Tian & Tingting Tong, 2021. "Generalized Mixtures of Exponential Distribution and Associated Inference," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    11. Mehdi Jabbari Nooghabi, 2021. "Comparing estimation of the parameters of distribution of the root density of plants in the presence of outliers," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.
    12. Amal S. Hassan & Said G. Nassr, 2019. "Power Lindley-G Family of Distributions," Annals of Data Science, Springer, vol. 6(2), pages 189-210, June.
    13. Ahlam H. Tolba & Chrisogonus K. Onyekwere & Ahmed R. El-Saeed & Najwan Alsadat & Hanan Alohali & Okechukwu J. Obulezi, 2023. "A New Distribution for Modeling Data with Increasing Hazard Rate: A Case of COVID-19 Pandemic and Vinyl Chloride Data," Sustainability, MDPI, vol. 15(17), pages 1-31, August.
    14. 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.
    15. Jiaxin Nie & Wenhao Gui, 2019. "Parameter Estimation of Lindley Distribution Based on Progressive Type-II Censored Competing Risks Data with Binomial Removals," Mathematics, MDPI, vol. 7(7), pages 1-15, July.
    16. Patawa, Rohit & Pundir, Pramendra Singh, 2023. "Inferential study of single unit repairable system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 503-516.
    17. 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.
    18. 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.
    19. Festus C. Opone & Nosakhare Ekhosuehi & Sunday E. Omosigho, 2022. "Topp-Leone Power Lindley Distribution(Tlpld): its Properties and Application," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 597-608, August.
    20. 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.

    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:gam:jmathe:v:8:y:2020:i:12:p:2146-:d:454753. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.