References
- Charalambides, C.A. (1986). On some properties of the linear function Poisson, binomial and negative binomial distributions. Metrika 33:203–216.
- Consul, P.C., Famoye, F. (2001). On Lagrange distributions of the second kind. Commun. Stat.–Theory Methods 30(1):165–178.
- Consul, P.C., Famoye, F. (2006). Lagrange Probability Distributions. New York: Birkhäuser.
- Consul, P.C., Shenton, L.R. (1972). Use of Lagrange expansion for generating discrete generalized probability distributions. SIAM J. Appl. Math. 23:239–248.
- Consul, P.C., Shenton, L.R. (1975). On the probabilistic structure and properties of discrete Lagrangian distributions. In: Patil, G.P., Kotz, S., Ord, J.K., eds. Statistical Distributions in Scientific Work, Vol.1, Models and Structures, (pp. 41–48). New York: North–Holland.
- Good, I.J. (1955). The joint distribution for the sizes of the generations in a cascade process. Math. Proc. Cambridge Philosophical Soc. 51:240–242.
- Imoto, T., Ong, S.H. (2013). A Lagrangian non central negative binomial distribution of the first kind. Commun. Stat.–Theory Methods 42:466–477.
- Jain, G.C., Consul, P.C. (1971). A generalized negative binomial distribution. SIAM J. Appl. Math. 21:501–513.
- Janardan, K.G. (1997). A wider class of Lagrange distributions of the second kind. Commun. Stat.–Theory Methods 26:2087–2091.
- Janardan, K.G., Rao, B.R. (1983). Lagrange distributions of the second kind and weighted distributions. SIAM J. Appl. Math. 43:302–313.
- Katayama, N. (1999). Performance analysis and optimization of a cyclic-service tandem queueing system with multi-class customers. Comput Math. Appl., 24:25–33.
- Kemp, A.W. (1979). Convolutions involving binomial pseudo-variables. Sankhyā, Series A 41:232–243.
- Kemp, A.W., Kemp, C.W. (1968). On a distribution associated with certain stochastic process. J. Royal Stat. Soc. Ser. B 30:160–163.
- Nair, S.S. (1971). A single server tandem queue. J. Appl. Probab. 8:95–109.
- Nelson, R.T. (1968). Dual-resource constrained series service systems. Operat. Res., 16:324–341.
- Ong, S.H., Chakraborty, S., Imoto, T., Shimizu, K. (2012). Generalizations of non-central negative binomial, Charlier series distributions and their extensions by Lagrange expansion. Commun. Stat.–Theory Methods 41:571–590.
- Otter, R. (1949). The multiplicative process. Annals Math. Stat. 45:360–363.
- Riordan, J. (1968). Combinatorial Identities.New York: Wiley.
- Sibuya, M., Miyawaki, N., Sumita, U. (1994). Aspects of Lagrangian probability distributions. J. Appl. Probab., 31:185–197.
- Takács, L. (1967). Combinatorial Methods in the Theory of Stochastic Process.New York: Wiley.
- Van Oyen, M. P., Teneketzis, D. (1994). Optimal stochastic scheduling of forest networks with switching penalties. Adv. Appl. Probab. 26:474–497.
- Yanagimoto, T. (1989). The inverse binomial distribution as a statistical model. Commun. Stat.–Theory Methods 18:3625–3633.