Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone

Statistical Science

Volumn 4, Issue 4, 1989, Pages 367-377

  Smith, Richard L ^a  

^a UNIVERSITY OF SURREY   (United Kingdom)

Author keywords

Atmospheric pollution; Clustered point processes; Environmental time series; Exceedances; Extreme values; Generalized extreme value distribution; Generalized pareto distribution; Maximum likelihood; Nonhomogeneous poisson process; Ozone; Return levels

Indexed keywords

EID: 84972496066     PISSN: 08834237     EISSN: None     Source Type: Journal    
DOI: 10.1214/ss/1177012400     Document Type: Article

References (35)

1. Davison, A. C. (1984). Modelling excesses over high thresholds, with an application. In Statistical Extremes and Applications (J. Tiago de Oliveira, ed.) 461-482. Reidel, Dordrecht.
2. 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.
3. Davison, A. C. and Smith, R. L. (1989). Models for exceedances over high thresholds. J. Roy. Statist. Soc. Ser. B. To appear.
4. Fisher, R. A. and Tippett, L. H. C. (1928). Limiting forms of the frequency distributions of the largest or smallest member of a sample. Proc. Cambridge Philos. Soc. 24 180-190.
5. Galambos, J. (1987). The Asymptotic Theory of Extreme Order Statistics, 2nd ed. Krieger, Melbourne, Fla.
6. Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d’une série aléatoire. Ann. of Math. (2) 44 423-453.
7. Gomes, M. I. (1981). An ¿-dimensional limiting distribution function of largest values and its relevance to the statistical theory of extremes. In Statistical Distributions in Scientific Work (C. Taillie, G. P. Patil and B. A. Baldessari, eds.) 6 389-410. Reidel, Dordrecht.
8. Gumbel, E. J. (1958). Statistics of Extremes. Columbia Univ. Press, New York.
9. Hill, B. M. (1975). A simple general approach to inference about the tail of a distribution. Ann. Statist. 3 1163-1174.
10. Horowitz, J. (1980). Extreme values from a nonstationary stochastic process: An application to air quality analysis (with discussion). Technometrics 22 469-482.
11. Hosking, J. R. M. (1985). Algorithm AS215: Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Appl. Statist. 34 301-310.
12. Hosking, J. R. M. and Wallis, J. R. (1987). Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 29 339-349.
13. Hosking, J. R. M., Wallis, J. R. and Wood, E. F. (1985). Estimation of the generalised extreme-value distribution by the method of probability-weighted moments. Technometrics 27 251-261.
14. Hüssler, J. (1986). Extreme values of non-stationary random sequences. J. Appl. Probab. 23 937-950.
15. Kendall, M. G. (1973). Time Series. Griffin, London.
16. Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983). Extremes and Related Properties of Random Sequences and Series. Springer, New York.
17. Leadbetter, M. R. and Rootzen, H. (1988). Extremal theory for stochastic processes. Ann. Probab. 16 431-478.
18. Nash, J. C. (1979). Compact Numerical Algorithms for Computers. Adam Hilger, Bristol.
19. NERC (1975). The Flood Studies Report. The Natural Environment Research Council, London.
20. Pickands, J. (1971). The two-dimensional Poisson process and extremal processes. J. Appl. Probab. 8 745-756.
21. Pickands, J. (1975). Statistical inference using extreme order statistics. Ann. Statist. 3 119-131.
22. Prescott, P. and Walden, A. T. (1980). Maximum likelihood estimation of the parameters of the generalized extreme value distribution. Biometrika 67 723-724.
23. Prescott, P. and Walden, A. T. (1983). Maximum likelihood estimation of the parameters of the three-parameter generalized extreme-value distribution from censored samples. J. Statist. Comput. Simulation 16 241-250.
24. Pugh, D. T. and Vassie, J. M. (1980). Applications of the joint probability method for extreme sea level computations. Proc. Inst. Civ. Engrs. Part 2 6 9 959-975.
25. Resnick, S. (1987). Extreme Values, Point Processes and Regular Variation. Springer, New York.
26. Roberts, E. M. (1979). Review of statistics of extreme values with applications to air quality data. Part I: Review. Part II: Applications. J. Air Pollution Control Assoc. 29 632-637, 733-740.
27. Singpurwalla, N. D. (1972). Extreme values from a lognormal law with application to air pollution problems. Technometrics 14 703-711.
28. Smith, R. L. (1984). Threshold methods for sample extremes. In Statistical Extremes and Applications (J. Tiago de Oliveira, ed.) 621-638. Reidel, Dordrecht.
29. Smith, R. L. (1985). Maximum likelihood estimation in a class of non-regular cases. Biometrika 72 67-92.
30. Smith, R. L. (1986). Extreme value theory based on the r largest annual events. J. Hydrology 86 27-43.
31. Tawn, J. A. (1988). An extreme value theory model for dependent observations. J. Hydrology 101 227-250.
32. Tawn, J. A. and Vassie, J. M. (1989). Extreme sea levels: The joint probability method revised and revisited. Proc. Inst. Civ. Engrs. Part 2. To appear.
33. Todorovic, P. and Zelenhasic, E. (1970). A stochastic model for flood analysis. Water Resources Research 6 1641-1648.
34. Weissman, I. (1975). Extremal processes generated by independent non-identically distributed random variables. Ann. Probab. 3 172-177.
35. Weissman, I. (1978). Estimation of parameters and large quantiles based on the k largest observations. J. Amer. Statist. Assoc. 73 812-815.