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Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t

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  • Jamalizadeh, A.
  • Mehrali, Y.
  • Balakrishnan, N.

Abstract

In this paper, we derive recurrence relations for cumulative distribution functions (cdf's) of bivariate t and extended skew-t distributions. These recurrence relations are over [nu] (the degrees of freedom), and starting from the known results for [nu]=1 and [nu]=2, they will allow for the recursive evaluation of the distribution function for any other positive integral value of [nu]. Then, we consider a linear combination of order statistics from a bivariate t distribution with an arbitrary mean vector and show that its cdf is a mixture of cdf's of the extended skew-t distributions. This mixture form, along with the explicit expressions of the cdf's of the extended skew-t distributions, enables us to derive explicit expressions for the cdf of the linear combination for any positive integral value of [nu].

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  • Jamalizadeh, A. & Mehrali, Y. & Balakrishnan, N., 2009. "Recurrence relations for bivariate t and extended skew-t distributions and an application to order statistics from bivariate t," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4018-4027, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4018-4027
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    References listed on IDEAS

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    Cited by:

    1. Boris Beranger & Simone A. Padoan & Scott A. Sisson, 2017. "Models for Extremal Dependence Derived from Skew-symmetric Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 21-45, March.
    2. 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.
    3. Mahdi Salehi & Ahad Jamalizadeh & Mahdi Doostparast, 2014. "A generalized skew two-piece skew-elliptical distribution," Statistical Papers, Springer, vol. 55(2), pages 409-429, May.
    4. Ali Genç, 2012. "Distribution of linear functions from ordered bivariate log-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 865-874, November.
    5. Marcel Bräutigam & Marie Kratz, 2018. "On the Dependence between Quantiles and Dispersion Estimators," Working Papers hal-02296832, HAL.
    6. Jamalizadeh, A. & Balakrishnan, N., 2009. "Prediction in a trivariate normal distribution via a linear combination of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2289-2296, November.
    7. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "A robust extension of the bivariate Birnbaum–Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 418-435.
    8. R. Arellano-Valle & Ahad Jamalizadeh & H. Mahmoodian & N. Balakrishnan, 2014. "$$L$$ L -statistics from multivariate unified skew-elliptical distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 559-583, May.
    9. Jamalizadeh, A. & Balakrishnan, N. & Salehi, Mehdi, 2010. "Order statistics and linear combination of order statistics arising from a bivariate selection normal distribution," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 445-451, March.
    10. Marcel, Bräutigam & Marie, Kratz, 2018. "On the Dependence between Quantiles and Dispersion Estimators," ESSEC Working Papers WP1807, ESSEC Research Center, ESSEC Business School.

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