IDEAS home Printed from https://ideas.repec.org/a/spr/aodasc/v12y2025i1d10.1007_s40745-023-00511-2.html
   My bibliography  Save this article

On Modeling Bivariate Lifetime Data in the Presence of Inliers

Author

Listed:
  • Sumangal Bhattacharya

    (Indian Institute of Technology Tirupati)

  • Ishapathik Das

    (Indian Institute of Technology Tirupati)

  • Muralidharan Kunnummal

    (The Maharaja Sayajirao University of Baroda)

Abstract

Many items fail instantaneously or early in life-testing experiments, mainly in electronic parts and clinical trials, due to faulty construction, inferior quality, or non-response to treatments. We record the observed lifetime as zero or near zero, defined as instantaneous or early failure observations. In general, some observations may be concentrated around a point, and others follow some continuous distribution. In data, these kinds of observations are regarded as inliers. Some unimodal parametric distributions, such as Weibull, gamma, log-normal, and Pareto, are usually used to fit the data for analyzing and predicting future events concerning lifetime observations. The usual modelling approach based on uni-modal parametric distributions may not provide the expected results for data with inliers because of the multi-modal nature of the data. The correlated bivariate observations with inliers also frequently occur in life-testing experiments. Here, we propose a method of modelling bivariate lifetime data with instantaneous and early failure observations. A new bivariate distribution is constructed by combining the bivariate uniform and bivariate Weibull distributions. The bivariate Weibull distribution has been obtained by using a 2-dimensional copula, assuming that the marginal distribution is a two-parametric Weibull distribution. An attempt has also been made to derive some properties (viz. joint probability density function, survival (reliability) function, and hazard (failure rate) function) of the modified bivariate Weibull distribution so obtained. The model’s unknown parameters have been estimated using a combination of the Maximum Likelihood Estimation technique and machine learning clustering algorithm, viz. Density-Based Spatial Clustering of Applications with Noise (DBSCAN). Numerical examples are provided using simulated data to illustrate and test the performance of the proposed methodologies. Relevant codes and necessary computations have been developed using R and Python languages. The proposed method has been applied to real data with possible inflation. It has been observed that the data contain inliers with a probability of 0.57. The study also does a comparison test with the proposed method and the existing method in the literature, wherein it was found that the proposed method provides a significantly better fit than the base model (in literature) with a P value less than 0.0001.

Suggested Citation

  • Sumangal Bhattacharya & Ishapathik Das & Muralidharan Kunnummal, 2025. "On Modeling Bivariate Lifetime Data in the Presence of Inliers," Annals of Data Science, Springer, vol. 12(1), pages 1-22, February.
    • Handle: RePEc:spr:aodasc:v:12:y:2025:i:1:d:10.1007_s40745-023-00511-2
    DOI: 10.1007/s40745-023-00511-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40745-023-00511-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40745-023-00511-2?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
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Pedro L. Ramos & Francisco Louzada, 2019. "A Distribution for Instantaneous Failures," Stats, MDPI, vol. 2(2), pages 1-12, May.
    2. Aisha Fayomi & Ehab M. Almetwally & Maha E. Qura, 2023. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    3. Philipp Arbenz, 2013. "Bayesian Copulae Distributions, with Application to Operational Risk Management—Some Comments," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 105-108, March.
    4. Lai, C. D. & Xie, M., 2000. "A new family of positive quadrant dependent bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 46(4), pages 359-364, February.
    5. Prabhashi W. Withana Gamage & Monica Chaudari & Christopher S. McMahan & Edwin H. Kim & Michael R. Kosorok, 2020. "An extended proportional hazards model for interval-censored data subject to instantaneous failures," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 158-182, January.
    6. Ehab Mohamed Almetwally & Hiba Zeyada Muhammed & El-Sayed A. El-Sherpieny, 2020. "Bivariate Weibull Distribution: Properties and Different Methods of Estimation," Annals of Data Science, Springer, vol. 7(1), pages 163-193, March.
    7. K. Muralidharan & P. Lathika, 2006. "Analysis of Instantaneous and Early Failures in Weibull Distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(3), pages 305-316, December.
    8. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
    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. Ehab M. Almetwally, 2022. "The Odd Weibull Inverse Topp–Leone Distribution with Applications to COVID-19 Data," Annals of Data Science, Springer, vol. 9(1), pages 121-140, February.
    2. El-Sayed A. El-Sherpieny & Hiba Z. Muhammed & Ehab M. Almetwally, 2024. "Progressive Type-II Censored Samples for Bivariate Weibull Distribution with Economic and Medical Applications," Annals of Data Science, Springer, vol. 11(1), pages 51-85, February.
    3. El-Sayed A. El-Sherpieny & Hiba Z. Muhammed & Ehab M. Almetwally, 2024. "Data Analysis by Adaptive Progressive Hybrid Censored Under Bivariate Model," Annals of Data Science, Springer, vol. 11(2), pages 507-548, April.
    4. Dina A. Ramadan & Ehab M. Almetwally & Ahlam H. Tolba, 2023. "Statistical Inference to the Parameter of the Akshaya Distribution under Competing Risks Data with Application HIV Infection to AIDS," Annals of Data Science, Springer, vol. 10(6), pages 1499-1525, December.
    5. Hiba Z. Muhammed & Ehab M. Almetwally, 2023. "Bayesian and Non-Bayesian Estimation for the Bivariate Inverse Weibull Distribution Under Progressive Type-II Censoring," Annals of Data Science, Springer, vol. 10(2), pages 481-512, April.
    6. Mohamed Ibrahim & Khaoula Aidi & M. Masoom Ali & Haitham M. Yousof, 2023. "A Novel Test Statistic for Right Censored Validity under a new Chen extension with Applications in Reliability and Medicine," Annals of Data Science, Springer, vol. 10(5), pages 1285-1299, October.
    7. Govinda Prasad Dhungana & Arun Kumar Chaudhary & Ramesh Prasad Tharu & Vijay Kumar, 2025. "Generalized Alpha Power Inverted Weibull Distribution: Application of Air Pollution in Kathmandu, Nepal," Annals of Data Science, Springer, vol. 12(5), pages 1691-1715, October.
    8. Heba Soltan Mohamed & M. Masoom Ali & Haitham M. Yousof, 2023. "The Lindley Gompertz Model for Estimating the Survival Rates: Properties and Applications in Insurance," Annals of Data Science, Springer, vol. 10(5), pages 1199-1216, October.
    9. Roberto Moro-Visconti & Salvador Cruz Rambaud & Joaquín López Pascual, 2023. "Artificial intelligence-driven scalability and its impact on the sustainability and valuation of traditional firms," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 10(1), pages 1-14, December.
    10. Mansoureh Beheshti Nejad & Seyed Mahmoud Zanjirchi & Seyed Mojtaba Hosseini Bamakan & Negar Jalilian, 2024. "Blockchain Adoption in Operations Management: A Systematic Literature Review of 14 Years of Research," Annals of Data Science, Springer, vol. 11(4), pages 1361-1389, August.
    11. Amaal Elsayed Mubarak & Ehab Mohamed Almetwally, 2024. "Modelling and Forecasting of Covid-19 Using Periodical ARIMA Models," Annals of Data Science, Springer, vol. 11(4), pages 1483-1502, August.
    12. Xueyan Xu & Fusheng Yu & Runjun Wan, 2023. "A Determining Degree-Based Method for Classification Problems with Interval-Valued Attributes," Annals of Data Science, Springer, vol. 10(2), pages 393-413, April.
    13. Qinghua Zheng & Chutong Yang & Haijun Yang & Jianhe Zhou, 2020. "A Fast Exact Algorithm for Deployment of Sensor Nodes for Internet of Things," Information Systems Frontiers, Springer, vol. 22(4), pages 829-842, August.
    14. Prashant Singh & Prashant Verma & Nikhil Singh, 2022. "Offline Signature Verification: An Application of GLCM Features in Machine Learning," Annals of Data Science, Springer, vol. 9(6), pages 1309-1321, December.
    15. Elham Shamsinejad & Touraj Banirostam & Mir Mohsen Pedram & Amir Masoud Rahmani, 2025. "A Review of Anonymization Algorithms and Methods in Big Data," Annals of Data Science, Springer, vol. 12(1), pages 253-279, February.
    16. Hui Zheng & Peng LI & Jing HE, 2022. "A Novel Association Rule Mining Method for Streaming Temporal Data," Annals of Data Science, Springer, vol. 9(4), pages 863-883, August.
    17. Sankalp Loomba & Madhavi Dave & Harshal Arolkar & Sachin Sharma, 2024. "Sentiment Analysis using Dictionary-Based Lexicon Approach: Analysis on the Opinion of Indian Community for the Topic of Cryptocurrency," Annals of Data Science, Springer, vol. 11(6), pages 2019-2034, December.
    18. Mathew P. M. Ashlin & P. G. Sankaran & E. P. Sreedevi, 2025. "Semiparametric Regression Analysis of Panel Count Data with Multiple Modes of Recurrence," Annals of Data Science, Springer, vol. 12(2), pages 571-590, April.
    19. Muhammed Navas Thorakkattle & Shazia Farhin & Athar Ali khan, 2022. "Forecasting the Trends of Covid-19 and Causal Impact of Vaccines Using Bayesian Structural time Series and ARIMA," Annals of Data Science, Springer, vol. 9(5), pages 1025-1047, October.
    20. Muhamad Redha Iqbal Bin Daud & Norhidayah Abdullah & Lovelyna Benedict Jipiu, 2025. "Determining the Correlation among the Users' Satisfaction and Familiarity with Malay Entrepreneurs Food Delivery Mobile Applications in Malaysia," Annals of Data Science, Springer, vol. 12(5), pages 1431-1462, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:aodasc:v:12:y:2025:i:1:d:10.1007_s40745-023-00511-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.