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Journal of Probability and Statistics
Volume 2016, Article ID 6385712, 7 pages
http://dx.doi.org/10.1155/2016/6385712
Research Article

Multivariate Macdonald Distribution and Its Properties

Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53–108, Medellín, Colombia

Received 31 July 2016; Revised 18 October 2016; Accepted 30 October 2016

Academic Editor: Ramón M. Rodríguez-Dagnino

Copyright © 2016 Daya K. Nagar et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. K. Nagar, A. Roldán-Correa, and A. K. Gupta, “Extended matrix variate gamma and beta functions,” Journal of Multivariate Analysis, vol. 122, pp. 53–69, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. D. K. Nagar, A. Roldán-Correa, and A. K. Gupta, “Matrix variate Macdonald distribution,” Communications in Statistics: Theory and Methods, vol. 45, no. 5, pp. 1311–1328, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  3. M. Aslam Chaudhry and S. M. Zubair, “On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms,” Journal of Computational and Applied Mathematics, vol. 55, no. 1, pp. 99–123, 1994. View at Publisher · View at Google Scholar
  4. M. Aslam Chaudhry and S. M. Zubair, “Generalized incomplete gamma functions with applications,” Journal of Computational and Applied Mathematics, vol. 55, no. 1, pp. 99–124, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. M. Aslam Chaudhry and S. M. Zubair, “Extended gamma and digamma functions,” Fractional Calculus & Applied Analysis, vol. 4, no. 3, pp. 303–324, 2001. View at Google Scholar · View at MathSciNet
  6. M. Aslam Chaudhry and S. M. Zubair, “Extended incomplete gamma functions with applications,” Journal of Mathematical Analysis and Applications, vol. 274, no. 2, pp. 725–745, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. Aslam Chaudhry and S. M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2002. View at Publisher · View at Google Scholar
  8. M. Aslam Chaudhry and S. M. Zubair, “On an extension of generalized incomplete gamma functions with applications,” Journal of the Australian Mathematical Society, Series B: Applied Mathematics, vol. 37, no. 3, pp. 392–405, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  9. D. K. Nagar, E. Zarrazola, and L. E. Sánchez, “Product and ratio of Macdonald random variables,” International Journal of Mathematical Analysis, vol. 10, no. 13, pp. 639–649, 2016. View at Publisher · View at Google Scholar
  10. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions. Vol. 1, Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1994.
  11. S. Kotz, N. Balakrishnan, and N. L. Johnson, Continuous Multivariate Distributions: Models and Applications, vol. 1 of Wiley Series in Probability and Statistics, John Wiley & Sons, New York, NY, USA, 2nd edition, 2000. View at Publisher · View at Google Scholar
  12. A. K. Gupta and D. K. Nagar, Matrix Variate Distributions, Chapman & Hall/CRC, Boca Raton, Fla, USA, 2000.
  13. S. L. Kalla, B. N. Al-Saqabi, and H. G. Khajah, “A unified form of gamma-type distributions,” Applied Mathematics and Computation, vol. 118, no. 2-3, pp. 175–187, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. F. Al-Musallam and S. L. Kalla, “Asymptotic expansions for generalized gamma and incomplete gamma functions,” Applicable Analysis, vol. 66, no. 1-2, pp. 173–187, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  15. F. Al-Musallam and S. L. Kalla, “Further results on a generalized gamma function occurring in diffraction theory,” Integral Transforms and Special Functions, vol. 7, no. 3-4, pp. 175–190, 1998. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. A. K. Gupta, D. K. Nagar, and L. Estela Sánchez, “Properties of matrix variate confluent hypergeometric function distribution,” Journal of Probability and Statistics, vol. 2016, Article ID 2374907, 12 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. D. K. Nagar, E. Zarrazola, and L. E. Sánchez, “A bivariate distribution whose marginal laws are gamma and Macdonald,” International Journal of Mathematical Analysis, vol. 10, no. 10, pp. 455–467, 2016. View at Publisher · View at Google Scholar
  18. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Elsevier/Academic Press, Amsterdam, The Netherlands, 8th edition, Translation edited and with a preface by Daniel Zwillinger and Victor Moll, 2015.
  19. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, vol. 2 of Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1995.