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Multivariate distributions with support above the diagonal

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  • M. C. Jones
  • P. V. Larsen

Abstract

A general family of distributions for the empirical modelling of ordered multivariate data is proposed. The family is based on, but greatly extends, the joint distribution of order statistics from an independent and identically distributed univariate sample. General properties, including marginal and conditional distributions, bivariate dependence, limiting distributions and links to the Dirichlet distribution are described. Univariate and bivariate special cases of the multivariate distributions, the latter including an equivalent rotated version, are considered. Two particular tractable special cases are stressed. The models are successfully and usefully fitted, by maximum likelihood, to meteorological data. The models are also applicable to data in which one variable is unconstrained and the other are all nonnegative. Copyright 2004, Oxford University Press.

Suggested Citation

  • M. C. Jones & P. V. Larsen, 2004. "Multivariate distributions with support above the diagonal," Biometrika, Biometrika Trust, vol. 91(4), pages 975-986, December.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:4:p:975-986
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    File URL: http://hdl.handle.net/10.1093/biomet/91.4.975
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    Citations

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    Cited by:

    1. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    2. C. Paddy Farrington & Mounia N. Hocine, 2010. "Within‐individual dependence in self‐controlled case series models for recurrent events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(3), pages 457-475, May.
    3. 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.
    4. Catana, Luigi-Ionut, 2022. "Stochastic orders of multivariate Jones–Larsen distribution family with empirical applications in physics, economy and social sciences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    5. M. C. Jones, 2015. "On Families of Distributions with Shape Parameters," International Statistical Review, International Statistical Institute, vol. 83(2), pages 175-192, August.
    6. Balakrishnan, Narayanaswamy & Ristić, Miroslav M., 2016. "Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 194-207.
    7. José María Sarabia & Vanesa Jordá & Faustino Prieto & Montserrat Guillén, 2020. "Multivariate Classes of GB2 Distributions with Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.

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