Some Models for Discretized Series of Events

Journal of the American Statistical Association

Volumn 91, Issue 434, 1996, Pages 601-609

  Davison, A C ^a   Ramesh, N I ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF GREENWICH   (United Kingdom)

Author keywords

Air pollution; Binary time series; Markov modulated Poisson process; Wet deposition; Zero probability function

Indexed keywords

EID: 0030547794     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476929     Document Type: Article

References (42)

1. ApSimon, H. M., and Davison, A. C. (1986), –A Statistical Model for Deriving Probability Distributions of Contamination for Accidental Releases,— Atmospheric Environment, 20, 1249-1259.
2. ApSimon, H. M., Goddard, A. I. H., and Wrigley, J. (1985), –Long-Range Transport of Radioisotopes-I. The MESOS Model,— Atmospheric Environment, 19, 99-111.
3. Chang, T. I., Kavvas, M. L., and Delleur, I. W. (1984), –Daily Precipitation Modeling by Discrete Autoregressive Moving Average Processes,— Water Resources Research, 20, 565-580.
4. Coles, S. G., and Tawn, J. A. (1996), –Modeling Extremes of the Areal Rainfall Process,— Journal of the Royal Statistical Society, Ser. B, 58, 329-347.
5. Cox, D. R. (1955), –Some Statistical Methods Connected With Series of Events— (with discussion), Journal of the Royal Statistical Society, Ser. B, 17, 129-164.
6. Cox, D. R., and Isham, V. S. (1980), Point Processes, London: Chapman and Hall.
7. Cox, D. R., and Isham, V. S. (1988), –A Simple Spatial-Temporal Model of Rainfall,— Proceedings of the Royal Society of London, Ser. A, 415, 317-328.
8. Cox, D. R., and Lewis, P. A. W. (1966), The Statistical Analysis of Series of Events, London: Chapman and Hall.
9. Davison, A. C. (1984a), Contribution to the discussion of –A Model-Fitting Analysis of Daily Rainfall Data,— by R. D. Stem and R. Coe, Journal of the Royal Statistical Society, Ser. A, 147, 26.
10. Davison, A. C. (1984b), –A Statistical Model for Contamination due to LongRange Atmospheric Transport of Radionuclides,— unpublished Ph. D. thesis, Imperial College, London.
11. Davison, A. c., and Hemphill, M. W. (1987), –On the Statistical Analysis of Ambient Ozone Data When Measurements are Missing,— Atmospheric Environment, 21, 629-639.
12. Davison, A. C, and Ramesh, N. I. (1993), –A Stochastic Model for Times of Exposures to Air Pollution From a Point Source,— in Statistics for the Environment, eds. V. Barnett and K. F. Turkman, New York: John Wiley, pp. 123-138.
13. Davison, A. C, and Smith, R. L. (1990), –Models for Exceedances Over High Thresholds— (with discussion), Journal of the Royal Statistical Society, Ser. B, 52, 393-442.
14. Diggle, P. J., and Milne, R. K. (1983), –Bivariate Cox Processes: Some Models for Bivariate Spatial Point Patterns,— Journal of the Royal Statistical Society, Ser. B, 45, 11-21.
15. Foufoula-Georgiou, E., and Lettenmaier, D. P. (1986), –Continuous-Time Versus Discrete-Time Point Process Models for Rainfall Occurrence Series,— Water Resources Research, 22, 531-542.
16. Foufoula-Georgiou, E., and Lettenmaier, D. P. (1987), –A Markov Renewal Model for Rainfall Occurrences,— Water Resources Research, 23, 875-884.
17. Gabriel, K. R., and Neumann, J. (1962), –A Markov Chain Model for Daily Rainfall Occurrence at Tel Aviv,— Quarterly Journal of the Royal Meteorological Society, 83, 90-95.
18. Green, J. R. (1964), –A Model for Rainfall Occurrence,— Journal of the Royal Statistical Society, Ser. B, 26, 345-353.
19. Green, J. R. (1967), –A Modified Model for Rainfall Occurrence,— Journal of the Royal Statistical Society, Ser. B, 29, 151-153.
20. Guttorp, P. (1986), –On Binary Time Series Obtained From ContinuousTime Point Processes Describing Rainfall,— Water Resources Research, 22, 897-904.
21. Hastie, T. J., and Tibshirani, R. J. (1990), Generalized Additive Models, London: Chapman and Hall.
22. Kedem, B. (1980), Binary Time Series, New York: Marcel Dekker.
23. Keenan, D. M. (1982), –A Time Series Analysis of Binary Data,— Journal of the American Statistical Association, 77, 816-821.
24. Kelly, F. P. (1979), Reversibility and Stochastic Processes, New York: John Wiley.
25. Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. (1986), Numerical Recipes: The Art of Scientific Computing, Cambridge, U. K.: Cambridge University Press.
26. Ramesh, N. I. (1992), –Statistical Inference for Some Classes of Cox Processes,— unpublished doctoral thesis, University of Oxford.
27. Ramesh, N. I. (1995), –Statistical Analysis on Markov-Modulated Poisson Processes,— Environmetrics, 6, 165-179.
28. Rodriguez-Iturbe, I., Cox, D. R., and Isham, V. S. (1987), –Some Models for Rainfall Based on Stochastic Point Processes,— Proceedings of the Royal Society of London, Ser. A, 410, 269-288.
29. Rodriguez-Iturbe, I., Cox, D. R., and Isham, V. S. (1988), –A Point Process Model for Rainfall: Further Developments,— Proceedings of the Royal Society of London, Ser. A, 417, 283-298.
30. Rohde, H., and Grandell, J. (1972), –On the Removal Time of Aerosol Particles From the Atmosphere by Precipitation Scavenging,— Tellus, 24, 442-454.
31. Rohde, H., and Grandell, J. (1981), –Estimates of Characteristic Times for Precipitation Scavenging,— Journal ofAtmospheric Science, 38, 370-386.
32. Self, S. G., and Liang, K.-Y. (1987), –Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests Under Nonstandard Conditions,— Journal of the American Statistical Association, 82, 605-610.
33. Smith, J. A. (1987), –Stochastic Modelling of Daily Rainfall Occurrences,— Water Resources Research, 23, 885-893.
34. Smith, I. A., and Karr, A. F. (1983), –A Point Process Model of Summer Rainfall,— Water Resources Research, 19, 95-103.
35. Smith, I. A., and Karr, A. F. (1985), –Statistical Inference for Point Process Models of Rainfall,— Water Resources Research, 21, 73-79.
36. Smith, R. L. (1984), Contribution to the discussion of –A Model-Fitting Analysis of Daily Rainfall Data,— by R. D. Stem and R. Coe, Journal of the Royal Statistical Society, Ser. A, 147, 24.
37. Stern, R. D., and Coe, R. (1984), –A Model-Fitting Analysis of Daily Rainfall Data— (with discussion), Journal ofthe Royal Statistical Society, Ser. A, 147, 1-34.
38. Tiao, G. c, Phadke, M. S., and Box, G. E. P. (1976), –Some Empirical Models for the Los Angeles Photochemical Smog Data,— Journal of the Air Pollution Control Association, 26, 485-490.
39. Waymire, E., and Gupta, V. (1981a), –The Mathematical Structure of Rainfall Representations, I, A Review of the Stochastic Rainfall Models,— Water Resources Research, 17, 1261-1272.
40. Waymire, E., and Gupta, V. (1981b), –The Mathematical Structure of Rainfall Representations, 2, A Review of the Theory of Point Processes,— Water Resources Research, 17, 1273-1285.
41. Waymire, E., and Gupta, V. (1981c), –The Mathematical Structure of Rainfall Representations, 3, Some Applications of the Point Process Theory to Rainfall Processes,— Water Resources Research, 17, 1287-1294.
42. Zucchini, W., and Guttorp, P. (1991), –A Hidden Markov Model for SpaceTime Precipitation,— Water Resources Research, 27, 1917-1923.