IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i2d10.1007_s00362-022-01328-6.html
   My bibliography  Save this article

The modality of skew t-distribution

Author

Listed:
  • Bader Alruwaili

    (Jouf University)

Abstract

The aims of this paper are to study the modality of skew t-distribution and the mixture of skew t-distributions graphically and analytically. We introduced a new formula to find the modes for univariate skew t-distribution and the mixture of univariate skew t-distribution. We also explored the effect of the skewness parameters and the degrees of freedom on the number and locations of modes for univariate skew t-distribution and in the mixture of skew t-distribution. Exploring the modes for the mixture of skew t-distribution helps the research to discover when and which components of the mixture can be merged in one homogeneous group to get the best results when exploring the data set.

Suggested Citation

  • Bader Alruwaili, 2023. "The modality of skew t-distribution," Statistical Papers, Springer, vol. 64(2), pages 497-507, April.
  • Handle: RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01328-6
    DOI: 10.1007/s00362-022-01328-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01328-6
    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/s00362-022-01328-6?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. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    2. Ray, Surajit & Ren, Dan, 2012. "On the upper bound of the number of modes of a multivariate normal mixture," Journal of Multivariate Analysis, Elsevier, vol. 108(C), pages 41-52.
    3. Adelchi Azzalini, 2001. "A note on regions of given probability of the skew-normal distribution," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 26-34.
    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. Yoosoon Chang & Yong-gun Kim & Boreum Kwak & Joon Y. Park, 2024. "Using Density Forecast for Growth-at-Risk to Improve Mean Forecast of GDP Growth in Korea," CAEPR Working Papers 2024-005 Classification-C, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.

    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. Azzalini, Adelchi, 2022. "An overview on the progeny of the skew-normal family— A personal perspective," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Padilla, Juan L. & Azevedo, Caio L.N. & Lachos, Victor H., 2018. "Multidimensional multiple group IRT models with skew normal latent trait distributions," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 250-268.
    3. Marco Minozzo & Luca Bagnato, 2021. "A unified skew‐normal geostatistical factor model," Environmetrics, John Wiley & Sons, Ltd., vol. 32(4), June.
    4. Redivo, Edoardo & Nguyen, Hien D. & Gupta, Mayetri, 2020. "Bayesian clustering of skewed and multimodal data using geometric skewed normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    5. Bernardi, Mauro, 2013. "Risk measures for skew normal mixtures," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1819-1824.
    6. Panagiotelis, Anastasios & Smith, Michael, 2010. "Bayesian skew selection for multivariate models," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1824-1839, July.
    7. Katherine Elizabeth Castellano & Andrew Dean Ho, 2013. "Contrasting OLS and Quantile Regression Approaches to Student “Growth†Percentiles," Journal of Educational and Behavioral Statistics, , vol. 38(2), pages 190-215, April.
    8. repec:wrk:wrkemf:27 is not listed on IDEAS
    9. 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.
    10. J. T. A. S. Ferreira & M. F. J. Steel, 2004. "On Describing Multivariate Skewness: A Directional Approach," Econometrics 0409010, University Library of Munich, Germany.
    11. Lachos, Victor H. & Prates, Marcos O. & Dey, Dipak K., 2021. "Heckman selection-t model: Parameter estimation via the EM-algorithm," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    12. Anna Gottard & Simona Pacillo, 2007. "On the impact of contaminations in graphical Gaussian models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 343-354, February.
    13. M. Teimourian & T. Baghfalaki & M. Ganjali & D. Berridge, 2015. "Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2233-2256, October.
    14. Fang, B.Q., 2006. "Sample mean, covariance and T2 statistic of the skew elliptical model," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1675-1690, August.
    15. Alexey Balaev, 2011. "Modeling multivariate parametric densities of financial returns (in Russian)," Quantile, Quantile, issue 9, pages 39-60, July.
    16. Massimo Bilancia & Giacomo Demarinis, 2014. "Bayesian scanning of spatial disease rates with integrated nested Laplace approximation (INLA)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 71-94, March.
    17. Anna Gottard & Simona Pacillo, 2007. "On the impact of contaminations in graphical Gaussian models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(3), pages 343-354, February.
    18. Huang Yangxin & Chen Ren & Dagne Getachew, 2011. "Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-28, January.
    19. Azzalini, Adelchi & Browne, Ryan P. & Genton, Marc G. & McNicholas, Paul D., 2016. "On nomenclature for, and the relative merits of, two formulations of skew distributions," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 201-206.
    20. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    21. 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.

    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:64:y:2023:i:2:d:10.1007_s00362-022-01328-6. 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.