On infinitely divisible exponential dispersion model related to poisson-exponential distribution

Communications in Statistics - Theory and Methods

Volumn 36, Issue 2, 2007, Pages 253-263

  Vinogradov, Vladimir ^a  

^a OHIO UNIVERSITY   (United States)

Author keywords

Bessel function; Branching process; Compound Poisson distribution; Confluent hypergeometric function; L vy measure; Local approximation; P lya Aeppli distribution; Poisson mixture; Power variance family; Rao damage process

Indexed keywords

APPROXIMATION THEORY; BESSEL FUNCTIONS; FUNCTION EVALUATION; MATHEMATICAL MODELS;

BRANCHING PROCESS; COMPOUND POISSON DISTRIBUTION; CONFLUENT HYPERGEOMETRIC FUNCTION; LEVY MEAUSURE; LOCAL APPROXIMATION; POISSON MIXTURE; POWER-VARIANCE FAMILY; RAO DAMAGE PROCESS;

POISSON DISTRIBUTION;

EID: 33847366705     PISSN: 03610926     EISSN: 1532415X     Source Type: Journal    
DOI: 10.1080/03610920600974534     Document Type: Article

References (18)

1. Abramowitz, M., Stegun, I. A. (1975). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover.
2. Dawson, D. A., Hochberg, K. J., Vinogradov, V. (1995). On path properties of super-2 processes II. In: Cranston, M. G., Pinsky, M. A., eds. Proceedings of Symposia in Pure Mathematics Series. Providence: AMS, pp. 385-403.
3. Dawson, D. A., Vinogradov, V. (1994). Almost-sure path properties of (2, d, β)-superprocesses. Stoch. Proc. Appl. 51:221-258.
4. Douglas, J. B. (1980). Analysis with Standard Contagious Distributions. Burtonsville, MD: International Co-operative Publishing House.
5. Dunn, P. K., Smyth, G. K. (2005). Series evaluation of Tweedie exponential dispersion model densities. Stat. Comput. 15:267-280.
6. Hougaard, P. (2000). Analysis of Multivariate Survival Data. New York: Springer.
7. Hougaard, P., Lee, M.-L. T., Whitmore, G. A. (1997). Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes. Biometrics 53:1225-1238.
8. Johnson, N. L., Kotz, S., Kemp, A. W. (2005). Univariate Discrete Distributions. 3rd ed. Hoboken, NJ: Wiley.
9. Jørgensen, B. (1997). The Theory of Dispersion Models. London: Chapman & Hall.
10. Jørgensen, B., Martínez, J. R., Tsao, M. (1994). Asymptotic behaviour of the variance function. Scand. J. Statist. 21:223-243.
11. Kendal, W. S. (2004). A scale invariant clustering of genes on human chromosome 7. BMC Evolutionary Biol. 4(3).
12. Kokonendji, C. C., Dossou-Gbété, S., Demétrio, C. G. B. (2004). Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demétrio classes. SORT; Statist. Operations Res. Trans. 28:201-214.
13. Küchler, U., Sørensen, M. (1997). Exponential Families of Stochastic Processes. New York: Springer.
14. Panjer, H. H., Willmot, G. E. (1992). Insurance Risk Models. Schaumburg, IL: Society of Actuaries.
15. Sato, K.-I. (1999). Levy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press.
16. Slater, L. J. (1960). Confluent Hypergeometric Functions. Cambridge: Cambridge University Press.
17. Smyth, G. K., Jørgensen, B. (2002). Fitting Tweedie's compound Poisson model to insurance claims data: dispersion modeling. Astin Bull. 32:143-157.
18. Vinogradov, V. (2004). On the power-variance family of probability distributions. Commun. Statist. Theor. Meth. 33:1007-1029 (Errata p. 2573).