IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v22y2017i4d10.1007_s13253-017-0301-x.html
   My bibliography  Save this article

The Odd Log-Logistic Student t Distribution: Theory and Applications

Author

Listed:
  • Altemir Silva Braga

    (Universidade de São Paulo)

  • Gauss M. Cordeiro

    (Universidade Federal de Pernambuco)

  • Edwin M. M. Ortega

    (Universidade de São Paulo)

  • Giovana O. Silva

    (Universidade Federal da Bahia)

Abstract

The normal distribution is most used in analysis of experiments. However, it is not suitable to apply in situations where the data have evidence of bimodality or heavier tails than the normal distribution. So, we propose a new four-parameter model called the odd log-logistic Student t distribution as an alternative to the normal and Student t distributions. The new distribution can be symmetric, platykurtic, mesokurtic or leptokurtic and may be unimodal or bimodal. Its various structural properties can be determined from the linear representation of its density function. The estimation of the model parameters is performed by maximum likelihood. The proposed distribution can be used as an alternative for randomized complete block design, thus providing analysis of real data more realistic than other special regression models. We perform a sensitivity analysis to detect influential or outlying observations, and construct generated envelopes from the residuals to select appropriate models. We illustrate the importance of the proposed model by means of three real data sets in analysis of experiments carried out in different regions of Brazil.

Suggested Citation

  • Altemir Silva Braga & Gauss M. Cordeiro & Edwin M. M. Ortega & Giovana O. Silva, 2017. "The Odd Log-Logistic Student t Distribution: Theory and Applications," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 615-639, December.
    • Handle: RePEc:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0301-x
    DOI: 10.1007/s13253-017-0301-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-017-0301-x
    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/s13253-017-0301-x?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. Nadarajah, Saralees & Gupta, Arjun K., 2007. "A generalized gamma distribution with application to drought data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 74(1), pages 1-7.
    2. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    3. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    4. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    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. Chénangnon Frédéric Tovissodé & Aliou Diop & Romain Glèlè Kakaï, 2021. "Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-31, April.
    2. Gauss Moutinho Cordeiro & Maria Do Carmo Soares De Lima & Edwin Moisés Marcos Ortega & Adriano Kamimura Suzuki, 2018. "A New Extended Birnbaum–Saunders Model: Properties, Regression and Applications," Stats, MDPI, vol. 1(1), pages 1-16, May.

    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. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    2. Mehrzad Ghorbani & Seyed Fazel Bagheri & Mojtaba Alizadeh, 2017. "A New Family of Distributions: The Additive Modified Weibull Odd Log-logistic-G Poisson Family, Properties and Applications," Annals of Data Science, Springer, vol. 4(2), pages 249-287, June.
    3. C. Adcock, 2010. "Asset pricing and portfolio selection based on the multivariate extended skew-Student-t distribution," Annals of Operations Research, Springer, vol. 176(1), pages 221-234, April.
    4. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    5. Lin, Tsung I. & Ho, Hsiu J. & Chen, Chiang L., 2009. "Analysis of multivariate skew normal models with incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2337-2351, November.
    6. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    7. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    8. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    9. Masoud Faridi & Majid Jafari Khaledi, 2022. "The polar-generalized normal distribution: properties, Bayesian estimation and applications," Statistical Papers, Springer, vol. 63(2), pages 571-603, April.
    10. Reinaldo B. Arellano-Valle & Marc G. Genton, 2010. "Multivariate extended skew-t distributions and related families," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 201-234.
    11. Jamalizadeh, A. & Balakrishnan, N., 2010. "Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1412-1427, July.
    12. Carol Alexander & Jose Maria Sarabia, 2010. "Endogenizing Model Risk to Quantile Estimates," ICMA Centre Discussion Papers in Finance icma-dp2010-07, Henley Business School, University of Reading.
    13. 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.
    14. Busetti, Fabio & Caivano, Michele & Delle Monache, Davide & Pacella, Claudia, 2021. "The time-varying risk of Italian GDP," Economic Modelling, Elsevier, vol. 101(C).
    15. Reinaldo B. Arellano-Valle & Adelchi Azzalini, 2022. "Some properties of the unified skew-normal distribution," Statistical Papers, Springer, vol. 63(2), pages 461-487, April.
    16. Koliai, Lyes, 2016. "Extreme risk modeling: An EVT–pair-copulas approach for financial stress tests," Journal of Banking & Finance, Elsevier, vol. 70(C), pages 1-22.
    17. Arellano-Valle, Reinaldo B. & Genton, Marc G. & Loschi, Rosangela H., 2009. "Shape mixtures of multivariate skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 91-101, January.
    18. Zubair Ahmad, 2020. "The Zubair-G Family of Distributions: Properties and Applications," Annals of Data Science, Springer, vol. 7(2), pages 195-208, June.
    19. 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.
    20. Mohsen Maleki & Darren Wraith & Reinaldo B. Arellano-Valle, 2019. "A flexible class of parametric distributions for Bayesian linear mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 543-564, 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:spr:jagbes:v:22:y:2017:i:4:d:10.1007_s13253-017-0301-x. 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.