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Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t

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Listed:
  • Jamalizadeh, A.
  • Khosravi, M.
  • Balakrishnan, N.

Abstract

In this note, we derive recurrence relations for the cumulative distribution function (cdf) of a skew-t distribution and also the distribution of a linear combination of order statistics arising from a bivariate-t distribution. These recurrence relations are over [nu], the degrees of freedom, and starting from the results for [nu]=1 and 2, they will allow for the recursive evaluation of the distribution function for any other value of [nu].

Suggested Citation

  • Jamalizadeh, A. & Khosravi, M. & Balakrishnan, N., 2009. "Recurrence relations for distributions of a skew-t and a linear combination of order statistics from a bivariate-t," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 847-852, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:847-852
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Marcel, Bräutigam & Marie, Kratz, 2018. "On the Dependence between Quantiles and Dispersion Estimators," ESSEC Working Papers WP1807, ESSEC Research Center, ESSEC Business School.
    5. 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.
    6. Ali Genç, 2012. "Distribution of linear functions from ordered bivariate log-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 865-874, November.
    7. 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.
    8. Marcel Bräutigam & Marie Kratz, 2018. "On the Dependence between Quantiles and Dispersion Estimators," Working Papers hal-02296832, HAL.
    9. 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.
    10. 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.

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