IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v102y2016icp23-36.html
   My bibliography  Save this article

Maximum likelihood estimation of triangular and polygonal distributions

Author

Listed:
  • Nguyen, Hien D.
  • McLachlan, Geoffrey J.

Abstract

Triangular distributions are a well-known class of distributions that are often used as elementary example of a probability model. In the past, enumeration and order statistics-based methods have been suggested for the maximum likelihood (ML) estimation of such distributions. A novel parametrization of triangular distributions is presented. The parametrization allows for the construction of an MM (minorization–maximization) algorithm for the ML estimation of triangular distributions. The algorithm is shown to both monotonically increase the likelihood evaluations, and be globally convergent. Using the parametrization is then applied to construct an MM algorithm for the ML estimation of polygonal distributions. This algorithm is shown to have the same numerical properties as that of the triangular distribution. Numerical simulations are provided to demonstrate the performances of the new algorithms against established enumeration and order statistics-based methods.

Suggested Citation

  • Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Maximum likelihood estimation of triangular and polygonal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 23-36.
    • Handle: RePEc:eee:csdana:v:102:y:2016:i:c:p:23-36
    DOI: 10.1016/j.csda.2016.04.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947316300561
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2016.04.003?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    2. Zhou, Hua & Zhang, Yiwen, 2012. "EM vs MM: A case study," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3909-3920.
    3. Hien Nguyen & Geoffrey McLachlan, 2015. "Maximum likelihood estimation of Gaussian mixture models without matrix operations," 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. 9(4), pages 371-394, December.
    4. Laura M. Sangalli & James O. Ramsay & Timothy O. Ramsay, 2013. "Spatial spline regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 681-703, September.
    5. Nguyen, Hien D. & McLachlan, Geoffrey J. & Wood, Ian A., 2016. "Mixtures of spatial spline regressions for clustering and classification," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 76-85.
    6. Small, Kenneth A. & Ng, Chen Feng, 2014. "Optimizing road capacity and type," Economics of Transportation, Elsevier, vol. 3(2), pages 145-157.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Xin & Liao, Qi & Wang, Qiang & Wang, Limin & Qiu, Rui & Liang, Yongtu & Zhang, Haoran, 2021. "How to promote zero-carbon oilfield target? A technical-economic model to analyze the economic and environmental benefits of Recycle-CCS-EOR project," Energy, Elsevier, vol. 225(C).

    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. Nguyen, Hien D. & McLachlan, Geoffrey J. & Ullmann, Jeremy F.P. & Janke, Andrew L., 2016. "Laplace mixture autoregressive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 18-24.
    2. Lloyd-Jones, Luke R. & Nguyen, Hien D. & McLachlan, Geoffrey J., 2018. "A globally convergent algorithm for lasso-penalized mixture of linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 19-38.
    3. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Linear mixed models with marginally symmetric nonparametric random effects," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 151-169.
    4. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    5. Ferraccioli, Federico & Sangalli, Laura M. & Finos, Livio, 2022. "Some first inferential tools for spatial regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. Marek Śmieja & Magdalena Wiercioch, 2017. "Constrained clustering with a complex cluster structure," 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. 11(3), pages 493-518, September.
    7. Giraldo, Ramón & Dabo-Niang, Sophie & Martínez, Sergio, 2018. "Statistical modeling of spatial big data: An approach from a functional data analysis perspective," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 126-129.
    8. Kenneth Lange & Eric C. Chi & Hua Zhou, 2014. "A Brief Survey of Modern Optimization for Statisticians," International Statistical Review, International Statistical Institute, vol. 82(1), pages 46-70, April.
    9. Arnone, Eleonora & Azzimonti, Laura & Nobile, Fabio & Sangalli, Laura M., 2019. "Modeling spatially dependent functional data via regression with differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 275-295.
    10. Hien Duy Nguyen & TrungTin Nguyen & Faicel Chamroukhi & Geoffrey John McLachlan, 2021. "Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.
    11. Smirnova, Ekaterina & Khormali, Omid & Egan, Joel M., 2019. "Functional analysis of spatial aggregation regions of Jeffrey pine beetle-attack within the Lake Tahoe Basin," Statistics & Probability Letters, Elsevier, vol. 144(C), pages 57-62.
    12. Xifen Huang & Chaosong Xiong & Tao Jiang & Junfeng Lu & Jinfeng Xu, 2022. "Efficient Estimation and Inference in the Proportional Odds Model for Survival Data," Mathematics, MDPI, vol. 10(18), pages 1-17, September.
    13. Diana, Tony, 2015. "An evaluation of departure throughputs before and after the implementation of wake vortex recategorization at Atlanta Hartsfield/Jackson International Airport: A Markov regime-switching approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 83(C), pages 216-224.
    14. Lee, Xing Ju & Hainy, Markus & McKeone, James P. & Drovandi, Christopher C. & Pettitt, Anthony N., 2018. "ABC model selection for spatial extremes models applied to South Australian maximum temperature data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 128-144.
    15. Kwun Chuen Gary Chan, 2017. "Acceleration of Expectation-Maximization algorithm for length-biased right-censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 102-112, January.
    16. Piercesare Secchi & Simone Vantini & Valeria Vitelli, 2015. "Rejoinder to the discussion of “Analysis of Spatio-Temporal Mobile Phone Data: a Case Study in the Metropolitan Area of Milan”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 335-338, July.
    17. Bernardi, Mara S. & Carey, Michelle & Ramsay, James O. & Sangalli, Laura M., 2018. "Modeling spatial anisotropy via regression with partial differential regularization," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 15-30.
    18. Xinyu Zhang & Jiguo Cao & Raymond J. Carroll, 2017. "Estimating varying coefficients for partial differential equation models," Biometrics, The International Biometric Society, vol. 73(3), pages 949-959, September.
    19. Mu Niu & Pokman Cheung & Lizhen Lin & Zhenwen Dai & Neil Lawrence & David Dunson, 2019. "Intrinsic Gaussian processes on complex constrained domains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 603-627, July.
    20. Ji Yeh Choi & Heungsun Hwang & Marieke E. Timmerman, 2018. "Functional Parallel Factor Analysis for Functions of One- and Two-dimensional Arguments," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 1-20, March.

    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:eee:csdana:v:102:y:2016:i:c:p:23-36. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.