Generalized gamma measures and shot-noise COX processes

Advances in Applied Probability

Volumn 31, Issue 4, 1999, Pages 929-953

  Brix, Anders ^a  

^a Guy Carpenter Instrat   (United Kingdom)

Author keywords

Cox process; Gamma measure; Gamma process; Neyman Scott process; Poisson cluster process; Random measure; Shot noise process; Spatial point process; Stable measure

Indexed keywords

EID: 0033333437     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1029955251     Document Type: Article

References (32)

1. Aalen, O (1992). Modelling heterogeneity in survival analysis by the compound Poisson distribution. Ann. App. Prob. 2, 951-972.
2. Baddeley, A. and MøLLER, J. (1989). Nearest-neighbour Markov point processes and random sets. Int. Stat. Rev. 57, 89-121.
3. Baddeley, a., Van Lieshout, M. and MøLLER, J. (1996). Markov properties of cluster processes. Adv. Appl. Prob. 28, 346-355.
4. Bar-Lev, S. and Enis, P. (1986). Reproducibility and natural exponential families with power variance functions. Ann. Statist. 14, 1507-1522.
5. BONDESSON, L. (1982). On simulation from infinitely divisible distributions. Adv. App. Prob. 14, 855-869.
6. BRIX, A. (1997). The P-G-family. Software libraries for C and S-plus. DINA Notat 61, Danish Informatic Network in Agriculture, Royal Veterinary and Agricultural College, Copenhagen, Denmark.
7. BRIX, A. and Chadœuf, F. (1998). Spatio-temporal modeling of weeds by shot-noise G Cox processes. Report 98-7, Department of Mathematics and Physics, Royal Veterinary and Agricultural University, Copenhagen.
8. CARTER, D. and Prenter, P. (1972). Exponential spaces and counting processes. Z. Wahrscheinlichkeitsth. 21, 1-19.
9. CHAMBERS, J., Malllows, C. and Stuck, B. (1976). A method for simulating stable random variables. J. Amer. Statist. Assoc. 71, 340-344.
10. DAIMEN, P., Laud, P., and Smith, A. (1995). Approximate random variate generation from infinitely divisible distributions with applications to bayesian inference. J. Roy. Statist. Soc. B 57, 547-563.
11. DALEY, D. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York.
12. DIGGLE, P. (1983). Statistical Analysis of Spatial Point Patterns. Academic Press, London.
13. GOULARD, M., Chadœuf, J. and Bertuzzi, P. (1994). Random boolean functions: Non-parametric estimation of the intensity, application to soil surface roughness. Statistics 25, 123-136.
14. HOUGAARD, P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387-396.
15. HOUGAARD, P., Lee, M. -L. and WHITMORE, G. (1997). Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes. Biometrics 53, 1225-1238.
16. JøRGENSEN, B (1987). Exponential dispersion models. J. Roy. Statist. Soc. B 49,127-162.
17. KALLENBERG, O (1983). Random Measures. Academic Press, London.
18. LARSEN, M. (1996). Point process models for weather radar image prediction. Ph.D. thesis, Royal Veterinary and Agricultural university, Copenhagen.
19. Le Cam, L. (1961). A stochastic description of precipitation. In Proceedings 4th Berkeley Symposium on Mathematical Statistics and Probability, ed. J. Neyman. Vol. 3 pp. 165-186.
20. Lee, M.-L. T. and WHITMORE, G. (1993). Stochastic processes directed by randomized time. J. Appl. Prob. 30, 302-314.
21. Lévy, P. (1954). Théorie de l’Addition des Variables Aléatoires. Gauthier-Villars, Paris.
22. MøLLER, J., Syversveen, A. and WAAGEPETERSEN, R. (1998). Log Gaussian Cox processes. Scand. J. Statist. 25, 451-482.
23. MORAN, P. (1959). The Theory of Storage. Methuen, London.
24. Rice, J. (1977). On generalized shot noise. Adv. Appl. Prob. 9, 553-565.
25. RIPLEY, B. (1987). Stochastic Simulation. Wiley, New York.
26. Ripley, B., and Kelly, F. (1977). Markov point processes. J. Lotidon Math. Soc. 15, 188-192.
27. SAMORODNITSKY, G and Taqqu, M. (1994). Stable Non-Gaussian Random Processes. Chapman & Hall, London.
28. STOYAN, D. and STOYAN, H. (1994). Fractals, Random Shapes and Point Fields. Wiley, New York.
29. STOYAN, D., KENDALL, W., and Mecke, J. (1995). Stochastic Geometry and its Applications. Wiley, New York.
30. TWEEDIE, M. (1984). An index which distinguishes between some important exponential families. In Statistics: Applications and New Directions, eds. J. Ghosh and J. Roy. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, pp. 579-604
31. VERE-JONES, D. and Davies. R. (1966). A statistical survey of earthquakes in the main seismic region of New Zealand. Part II, time series analysis. N.Z.J. Geol. Geophys. 9, 251-284.
32. WOLPERT, R. and ICKSTADT, K. (1998). Poisson/Gamma random field models for spatial statistics. Biometrika 85, 251-267.