References
- Adelson, R.M. (1966). Compound Poisson distributions. Oper. Res. 17(1):73–75.
- Barbour, A.D., Chen, L.H.Y., Loh, W.L. (1992). Compound Poisson approximation for nonnegative random variables via Stein’s method. Ann. Prob. 20(4):1843–1866.
- Bekelis, D. (1997). Convolutions of the Poisson laws in number theory. Analytic and Probabilistic Methods in Number Theory: Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23–27 September 1996. VSP International Science, Vol. 4, pp. 283–296.
- Bertoin, J. (1996). Lévy Processes.Cambridge: Cambridge University Press.
- Breur, L., Baum, D. (2005). An Introduction to Queueing Theory and Matrix-Analytic Methods.New York: Springer.
- Bret, C., Ionides, E.L. (2011). Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems. Stochastic Processes Appl. 121(11):2571–2591.
- Buchmann, B., Grübel, R. (2003). Decompounding: An estimation problem for Poisson random sums. Ann. Stat. 31(4):1054–1074.
- Cinlar, E. (2011). Probability and Stochastics. New York: Springer.
- Elliott, P.D.T.A. (1980). Probabilistic Number Theory II: Central Limit Theorems. New York: Springer.
- Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. I. 3rd ed. New York: Wiley.
- Fleming, T.R., Harrington, D.P. (1991). Counting Processes and Survival Analysis. New York: Wiley.
- Haight, F.A. (1967). Handbook of the Poisson Distribution. Los Angeles: Wiley.
- He, Q.M. (2014). Fundamentals of Matrix-Analytic Methods. New York: Springer.
- Kalashnikov, V.V. (1997). Geometric Sums: Bounds for Rare Events with Applications: Risk Analysis, Reliability, Queueing.New York: Springer.
- Lévy, P. (1934). Sur les intégrales dont les éléments sont des variables aléatoires indépendantes. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze. 3(3–4):337–366.
- Lévy, P. (1937). Sur les exponentielles de polynômes et sur l’arithmétique des produits de lois de Poisson. Annales scientifiques de l’École Normale Supérieure. 54:231–292.
- Johnson, N.L., Kemp, A.W., Kotz, S. (2005). Univariate Discrete Distributions. 3rd ed. NJ: Wiley.
- Jánossy, L., Rényi, A., Aczél, J. (1950). On composed Poisson distributions, I. Acta Math. Hungarica 1(2):209–224.
- Khintchine, A.Y. (1955). Mathematical methods of queuing theory. Proceedings of the Steklov Institute. VA Steklov, 49:3--122. [in Russian]
- Kemp, A.W. (1978). Slustep size probabilities for generalized Poisson distributions. Commun. Stat.—Theory. Methods 7(15):1433–1438.
- Kruglov, V.M. (2010). A characterization of the Poisson distribution. Stat. Prob. Lett. 80:2032–2034.
- Maceda, E.C. (1948). On the compound and generalized Poisson distributions. Ann. Math. Stat. 19(3):414–416.
- Patel, Y.C. (1976). Estimation of the parameters of the triple and quadruple stuttering-Poisson distributions. Technometrics 18(1):67–73.
- Pollaczek-Geiringer, H. (1928). Über die Poissonsche Verteilung und die Entwicklung willkürlicher Verteilungen. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 4(2):292–309.
- Puig, P., Valero, J. (2006). Count data distributions: some characterizations with applications. Journal of the American Statistical Association. 101(473): 332–340.
- Puri, P. S., Goldie, C. M. (1979). Poisson mixtures and quasi-infinite divisibility of distributions. Journal of Applied Probability.138–153.
- Steutel, F.W., Van Harn, K. (2003). Infinite Divisibility of Probability Distributions on the Real Line. New York: CRC Press.
- Satheesh, S., Sandhya, E., Abraham, T.L. (2010). Limit distributions of random sums of Z+-valued random variables. Commun. Stat.—Theory Methods 39(11):1979–1984.
- Sato, K. (2013). Lévy Processes and Infinitely Divisible Distributions. Revised edition. Cambridge: Cambridge University Press.
- van Harn, K. (1978). Classifying Infinitely Divisible Distributions by Functional Equations. Amsterdam: Mathematisch.
- Watanabe, S. (1964). On discontinuous additive functionals and Lévy measures of Markov processes. Jpn. J. Math. 14:53–70.
- Whittaker, J.M. (1937). The shot effect for showers. Mathematical Proceedings of the Cambridge Philosophical Society. 33:451--458. doi:10.1017/S0305004100077598
- Zhang, H., Liu, Y., Li, B. (2014). Notes on discrete compound Poisson model with applications to risk theory. Insurance: Mathematics and Economics 59:325—336.