On discrete distributions generated from drawing balls with bivariate labels

References

• Billingsley, P. 1995. Probability and measure. 3rd ed. New York: John Wiley and Sons, Inc.
   Google Scholar
• Borel, E., and A. Cheron. 1955. Théorie Mathématique du Bridge (A La Portée de Torus). Paris: Gauthiers-Villars.
   Google Scholar
• Charalambides, Ch. A. 2002. Enumerative combinatorics. Boca Raton: Chapman & Hall/CRC.
   Google Scholar
• Charalambides, Ch. A. 2005. Combinatorial methods in discrete distributions. New York: John Wiley & Sons.
   Google Scholar
• David, F. N., and D. E. Barton. 1962. Combinatorial chance. London: Charles Griffin & Co. Ltd.
   Google Scholar
• Durrett, R. 2010. Probability: Theory and Examples. 4th ed. Cambridge: Cambridge University Press.
   Google Scholar
• Eryilmaz, S. 2008. Run statistics defined on the multi-color urn model. Journal of Applied Probability 45:1007–23.
   Web of Science ®Google Scholar
• Eryilmaz, S., and M. Bekci. 2007. Runs in a bivariate sequence over the first coordinate. Communications in Statistics—Theory and Methods 36:1389–95.
   Web of Science ®Google Scholar
• Feller, W. 1968. An introduction to probability theory and its applications. Vol. I, 3rd ed. New York: Wiley.
   Google Scholar
• Frankowski, K., and M. Sobel. 2005. Solutions of some birthday problems using dirichlet integrals. Communications in Statistics Theory and Methods 34:1393–410.
   Web of Science ®Google Scholar
• Holst, L. 1986. On birthday, collectors’, occupancy and other classical urn problems. International Statistical Review 54:15–27.
   Web of Science ®Google Scholar
• Inoue, K., and S. Aki. 2008. Methods for studying generalized birthday and coupon collection problems. Communications in Statistics—Simulation and Computation 37:844–62.
   Web of Science ®Google Scholar
• Inoue, K., and S. Aki. 2009. On waiting time distributions associated with compound patterns in a sequence of multi-state trials. Annals of the Institute of Statistical Mathematics 61:499–516.
   Web of Science ®Google Scholar
• Inoue, K., and S. Aki. 2014. On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials. Metrika 77:895–920.
   Web of Science ®Google Scholar
• Johnson, N. L., and S. Kotz. 1977. Urn models and their applications. New York: Wiley.
   Google Scholar
• Johnson, N. L., S. Kotz, and N. Balakrishnan. 1997. Discrete multivariate distributions. New York: Wiley.
   Google Scholar
• Johnson, N. L., A. W. Kemp, and S. Kotz. 2005. Univariate discrete distributions. 3rd ed. New York: Wiley.
   Google Scholar
• Kaiser, H. F., and W. Stefansky. 1972. A Pólya distribution for teaching. The American Statistician 26:40–3.
   Web of Science ®Google Scholar
• Kim, S., and N. Flournoy. 2015. Optimal experimental design for systems with bivariate failures under a bivariate Weibull function. Journal of the Royal Statistical Society: Series C 64:413–32.
   Web of Science ®Google Scholar
• Kotz, S., and N. Balakrishnan. 1997. Advances in urn models during the past two decades. In Advances in combinatorial methods and applications to probability and statistics, ed. N. Balakrishnan, 203–57. Boston: Birkhäuser.
   Google Scholar
• Mahmoud, H. 2008. Pólya urn models. Boca Raton: CRC Press.
   Google Scholar
• Makri, F. S., A. N. Philippou, and Z. M. Psillakis. 2007a. Pólya, Inverse Pólya, and Circular Pólya distributions of order k for ℓ-overlapping success runs. Communications in Statistics—Theory and Methods 36:657–68.
   Web of Science ®Google Scholar
• Makri, F. S., A. N. Philippou, and Z. M. Psillakis. 2007b. Success run statistics defined on an urn model. Advances in Applied Probability 39:991–1019.
   Web of Science ®Google Scholar
• Marshall, A. W., and I. Olkin. 1990. Bivariate distributions generalized from Pólya-Eggenberger urn models. Journal of Multivariate Analysis 35:48–65.
   Web of Science ®Google Scholar
• Marshall, A. W., and I. Olkin. 1993. Bivariate life distributions from Pólya’s urn model for contagion. Journal of Applied Probability 30:497–508.
   Web of Science ®Google Scholar
• Sobel, M., and K. Frankowski. 1994. A duality theorem for solving multiple-player multivariate hypergeometric problems. Statistics & Probability Letters 20:155–62.
   Web of Science ®Google Scholar
• Sobel, M., and K. Frankowski. 1997. Venn Diagrams, Coupon Collections, Bingo Games and Dirichlet Distributions. In Advances in statistical decision theory and applications statistics for industry and technology, eds. S. Panchapakesan and N. Balakrishnan, 343–67. Boston: Birkhäuser.
   Google Scholar
• Sobel, M., and K. Frankowski. 2004. Extensions of Dirichlet integrals: Their computation and probability applications. In Handbook of beta distribution and its applications, eds. A. K. Gupta and S. Nadarajah, 319–60. New York: Marcel Dekker.
   Google Scholar