IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v66y2025i3d10.1007_s00362-025-01677-y.html
   My bibliography  Save this article

Bounded data modeling using logit-skew-normal mixtures

Author

Listed:
  • Abbas Mahdavi

    (Vali-e-Asr University of Rafsanjan)

  • Javier E. Contreras-Reyes

    (Universidad de Las Américas)

Abstract

Bounded data on (0, 1) have often been modelled in several real-world applications using several distributions. However, these studies lack addressing skewness, kurtosis and heavy-tailed properties in observations. This study presents a novel skew-normal type distribution defined within a bounded interval, which is derived by integrating the structures of skew-normal distributions and the logit function. With its extended skewness and bounded properties, the proposed model provides a versatile and suitable solution for modeling rates and proportions. We have developed an EM-type algorithm to accurately estimate the model parameters and its finite mixtures. To illustrate the effectiveness of our approach, we conducted experiments that included two simulation studies and an analysis of real data. The results highlight the flexibility and accuracy of our proposed model in comparison to traditional mixture models.

Suggested Citation

  • Abbas Mahdavi & Javier E. Contreras-Reyes, 2025. "Bounded data modeling using logit-skew-normal mixtures," Statistical Papers, Springer, vol. 66(3), pages 1-21, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01677-y
    DOI: 10.1007/s00362-025-01677-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-025-01677-y
    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/s00362-025-01677-y?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. Lee, Gyemin & Scott, Clayton, 2012. "EM algorithms for multivariate Gaussian mixture models with truncated and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2816-2829.
    2. Basso, Rodrigo M. & Lachos, Víctor H. & Cabral, Celso Rômulo Barbosa & Ghosh, Pulak, 2010. "Robust mixture modeling based on scale mixtures of skew-normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2926-2941, December.
    3. Cabral, Celso Rômulo Barbosa & Lachos, Víctor Hugo & Prates, Marcos O., 2012. "Multivariate mixture modeling using skew-normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 126-142, January.
    4. Cedric Flecher & Denis Allard & Philippe Naveau, 2010. "Truncated skew-normal distributions: moments, estimation by weighted moments and application to climatic data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 331-345.
    5. Mustafa Ç. Korkmaz, 2020. "A new heavy-tailed distribution defined on the bounded interval: the logit slash distribution and its application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(12), pages 2097-2119, September.
    6. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    7. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    8. Cook, Douglas O. & Kieschnick, Robert & McCullough, B.D., 2008. "Regression analysis of proportions in finance with self selection," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 860-867, December.
    9. Salah H. Abid & Uday J. Quaez & Javier E. Contreras-Reyes, 2021. "An Information-Theoretic Approach for Multivariate Skew- t Distributions and Applications," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
    10. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
    11. Emilio Gómez-Déniz & José María Sarabia, 2018. "A Family of Generalised Beta Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 5(3), pages 401-420, September.
    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. Francesca Condino & Filippo Domma, 2017. "A new distribution function with bounded support: the reflected generalized Topp-Leone power series distribution," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 51-68, April.
    2. Sharon Lee & Geoffrey McLachlan, 2013. "Model-based clustering and classification with non-normal mixture distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 427-454, November.
    3. Morris, Katherine & Punzo, Antonio & McNicholas, Paul D. & Browne, Ryan P., 2019. "Asymmetric clusters and outliers: Mixtures of multivariate contaminated shifted asymmetric Laplace distributions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 145-166.
    4. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    5. Latouche, Karine & Rouviere, Elodie, 2011. "Brokers vs. Retailers: Evidence from the French Imports Industry of Fresh Produce," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114398, European Association of Agricultural Economists.
    6. Christopher F. Baum & Mustafa Caglayan & Oleksandr Talavera, 2016. "R&D Expenditures and Geographical Sales Diversification," Manchester School, University of Manchester, vol. 84(2), pages 197-221, March.
    7. Jiong Liu & R. A. Serota, 2023. "Rethinking Generalized Beta family of distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(2), pages 1-14, February.
    8. Egger, Peter & Keuschnigg, Christian & Merlo, Valeria & Wamser, Georg, 2011. "Corporate Taxes, Internal Borrowing, and the Lending Capacity within Multinational Firms," Economics Working Paper Series 1142, University of St. Gallen, School of Economics and Political Science.
    9. Reboul, E. & Guérin, I. & Nordman, C.J., 2021. "The gender of debt and credit: Insights from rural Tamil Nadu," World Development, Elsevier, vol. 142(C).
    10. Peter Egger & Christian Keuschnigg & Valeria Merlo & Georg Wamser, 2014. "Corporate Taxes and Internal Borrowing within Multinational Firms," American Economic Journal: Economic Policy, American Economic Association, vol. 6(2), pages 54-93, May.
    11. Gambacorta, Leonardo & Mayordomo, Sergio & Serena Garralda, Jose-Maria, 2020. "Dollar borrowing, firm-characteristics, and FX-hedged funding opportunities," CEPR Discussion Papers 14419, C.E.P.R. Discussion Papers.
    12. Yana Melnykov & Xuwen Zhu & Volodymyr Melnykov, 2021. "Transformation mixture modeling for skewed data groups with heavy tails and scatter," Computational Statistics, Springer, vol. 36(1), pages 61-78, March.
    13. Prates, Marcos Oliveira & Lachos, Victor Hugo & Barbosa Cabral, Celso Rômulo, 2013. "mixsmsn: Fitting Finite Mixture of Scale Mixture of Skew-Normal Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i12).
    14. Juan C. Reboredo & Luis A. Otero González, 2022. "Low carbon transition risk in mutual fund portfolios: Managerial involvement and performance effects," Business Strategy and the Environment, Wiley Blackwell, vol. 31(3), pages 950-968, March.
    15. Sharon Lee & Geoffrey McLachlan, 2013. "On mixtures of skew normal and skew $$t$$ -distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 241-266, September.
    16. Ghosh Indranil & Dey Sanku & Kumar Devendra, 2019. "Bounded M-O Extended Exponential Distribution with Applications," Stochastics and Quality Control, De Gruyter, vol. 34(1), pages 35-51, June.
    17. Yang Yang & Lichun Wang, 2024. "A non-iteration Bayesian sampling algorithm for robust seemingly unrelated regression models $$^*$$ ∗," Computational Statistics, Springer, vol. 39(3), pages 1281-1300, May.
    18. Bluhm R & Crombrugghe D.P.I. de & Szirmai A., 2013. "The pace of poverty reduction - A fractional response approach," MERIT Working Papers 2013-051, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    19. Oberoi, Jaideep, 2018. "Interest rate risk management and the mix of fixed and floating rate debt," Journal of Banking & Finance, Elsevier, vol. 86(C), pages 70-86.
    20. Abbas Mahdavi & Anthony F. Desmond & Ahad Jamalizadeh & Tsung-I Lin, 2024. "Skew Multiple Scaled Mixtures of Normal Distributions with Flexible Tail Behavior and Their Application to Clustering," Journal of Classification, Springer;The Classification Society, vol. 41(3), pages 620-649, November.

    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:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01677-y. 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.