An extension of three-parameter Burr III distribution for low-flow frequency analysis

Computational Statistics and Data Analysis

Volumn 52, Issue 3, 2008, Pages 1304-1314

  Shao, Quanxi ^a   Chen, Yongqin D ^b   Zhang, Lu ^a  

^a CSIRO   (Australia)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Extended Burr III distribution; Fr chet distribution; Low flow frequency analysis; T year return level

Indexed keywords

AUSTRALIA; COMPUTER SIMULATION; DISTRIBUTION FUNCTIONS; MAXIMUM LIKELIHOOD ESTIMATION; METHOD OF MOMENTS; WATER RESOURCES;

EXTENDED BURR III DISTRIBUTION; FRECHET DISTRIBUTION; LOW FLOW FREQUENCY ANALYSIS; T YEAR RETURN LEVEL;

FREQUENCY ESTIMATION;

EID: 35548983060     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2007.06.014     Document Type: Article

References (43)

1. ANZECC and ARMCANZ (2000). Australian and New Zealand Guidelines for Fresh and Marine Water Quality. National Water Quality Management Strategy Paper No. 4. Australian and New Zealand Environment and Conservation Council & Agriculture and Resource Management Council of Australia and New Zealand, Canberra.
2. Balkema A.A., and de Haan L. Residual life time at great age. Ann. Probab. 2 5 (1974) 792-804
3. Burr I.W. Cumulative frequency functions. Ann. Math. Statist. 13 (1942) 215-232
4. 4. Comm. Statist. 2 (1973) 1-21
5. Chang M., and Boyer D.G. Estimates of low-flows using watershed and climatic parameters. Water Resources Res. 13 6 (1977) 997-1001
6. Cramér H. On the composition of elementary errors (second paper: statistical applications). Skandinavisk Aktuarietidskrift 11 (1928) 141-180
7. Davis P.J. Gamma function and related functions. In: Abramowitz M., and Stegun I.A. (Eds). Handbook of Mathematical Functions (1972), Dover, New York (Chapter 7)
8. Dingman S.L., and Lawlor S.C. Estimating low-flow quantiles from drainage-basin characteristics in New Hampshire and Vermont. Water Resources Bull. 31 2 (1995) 243-256
9. Giesbrecht F., and Kempthorne O. Maximum likelihood estimation in the three-parameter lognormal distribution. J. Roy. Statist. Soc. Ser. B Met. 38 3 (1976) 257-264
10. Greenwood J.A., Landwehr J.M., Matalas N.C., and Wallis J.R. Probability weighted moments: definition and relation to parameters of several distributions expressible in inverse form. Water Resources Res. 15 (1979) 1049-1054
11. Hatke M.A.S. A certain cumulative probability function. Ann. Math. Statist. 20 (1949) 461-463
12. Haynsworth E.V., and Goldberg K. Bernoulli and Euler polynomials, Riemann Zeta function. In: Abramowitz M., and Stegun I.A. (Eds). Handbook of Mathematical Functions (1972), Dover, New York (Chapter 23)
13. Hosking J.R.M. L-moments: analysis and estimation of distributions using linear combinations of order statistics. J. Roy. Statist. Soc. Ser. B 52 (1990) 105-124
14. Kroll C.N., and Vogel R.M. Probability distribution of low streamflow series in the United States. J. of Hydrologic Engrg. 7 2 (2002) 137-146
15. Lehmann E.L. The power of rank tests. Ann. Math. Statist. 24 (1953) 23-42
16. Lindsay S.R., Wood G.R., and Woollons R.C. Modelling the diameter distribution of forest stands using the Burr distribution. J. Appl. Statist. 23 (1996) 609-619
17. Matalas, N.C., 1963. Probability distribution of low-flows. USGS Professional Paper 434-A, USGS, Washington, DC.
18. Nathan R.J., and McMahon T.A. Practical aspects of low-flow frequency analysis. Water Resources Res. 26 9 (1990) 2135-2141
19. Pearson C.P. Regional frequency analysis of low flows in New Zealand rivers. J. of Hydrology 30 2 (1995) 53-64
20. Pearson E.S., and Hartley H.O. Biometrika Tables for Statisticians vol. 2 (1972), Cambridge University Press, Cambridge, UK
21. Pickands III J. Statistical inference using extreme order statistics. Ann. Statist. 3 (1975) 119-131
22. Riggs H.C. Characteristics of low flows. J. of Hydraulic Engrg. 106 5 (1980) 717-731
23. Rodriguez N. A guide to the Burr type XII distributions. Biometrika 64 (1977) 129-134
24. Shao Q. Estimation for hazardous concentrations based on NOEC toxicity data: an alternative approach. Environmetrics 11 5 (2000) 583-595
25. Shao Q. A reparameterisation method for embedded models. Comm. Statist. Theory Methods 31 (2002) 683-697
26. Shao Q. Maximum likelihood estimation for generalized logistic distributions. Comm. Statist. Theory Methods 31 10 (2002) 1687-1700
27. Shao Q. Notes on maximum likelihood estimation for the three-parameter Burr XII distribution. Comput. Statist. Data Anal. 45 (2004) 675-687
28. Shao Q., Ip W.-C., and Wong H. Determination of embedded distribution. Comput. Statist. Data Anal. 46 (2004) 317-334
29. Shao Q., Wong H., Xia J., and Ip W.C. Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis. Hydrological Sci. J. 49 4 (2004) 685-702
30. Singh K.P., and Stall J.B. Hydrology of 7-day 10-yr low flows. J. of Hydraulic Division, ASCE HY12 (1977) 1753-1771
31. Smakhtin V.U. Low flow hydrology: a review. J. of Hydrology 240 (2001) 147-186
32. 2. C. R. Acad. Sci. Paris 202 (1936) 449-452
33. 2: criterion of von Mises. Rec. Math. 2 (1937) 973-993
34. Tadikamalla P.R. A look at the Burr and related distributions. Internat. Statist. Rev. 48 (1980) 337-344
35. Vogel R.M., and Kroll C.N. Low-flow frequency analysis using probability-plot correlation coefficients. J. Water Resour. Plann. Manage. 115 3 (1989) 338-357
36. Vogel R.M., and Kroll C.N. Regional geohydrologic-geomorphic relationships for estimation of low-flow statistics. Water Resources Res. 28 9 (1992) 2451-2458
37. Vogel R.M., and Wilson I. Probability distribution of annual maximum, mean and minimum streamflows in the United States. J. of Hydrologic Engrg. 1 2 (1996) 69-76
38. Von Mises, R., 1931. Wabrscheinlichkeitsrechnung und ibre Anwendung in der Statistik und theoretischen Physik. Leipzig, Deuticke.
39. Wang F.K., Keats J.B., and Zimmer W.J. Maximum likelihood estimation of the Burr XII distribution with censored and uncensored data. Microelectron. Reliability 36 (1996) 359-362
40. Watkins A.J. An algorithm for maximum likelihood estimation in the three parameter Burr XII distribution. Comput. Statist. Data Anal. 32 (1999) 19-27
41. Wingo D.R. Maximum likelihood estimation of Burr XII distribution parameters under type II censoring. Microelectron. Reliability 33 (1993) 1251-1257
42. WMO, 1974. International Glossary of Hydrology. World Meteorological Organisation, Geneva.
43. Zimmer W.J., Keats J.B., and Wang F.K. The Burr XII distribution in reliability analysis. J. Qual. Tech. 30 (1998) 386-394