Approximation of modified Anderson-Darling test statistics for extreme value distributions with unknown shape parameter

Journal of Hydrology

Volumn 499, Issue , 2013, Pages 41-49

  Heo, Jun Haeng ^a   Shin, Hongjoon ^a   Nam, Woosung ^a   Om, Juseong ^a   Jeong, Changsam ^b  

^a Yonsei University   (South Korea)

^b Induk University   (South Korea)

Author keywords

Critical value; Goodness of fit test; Modified Anderson Daring test; Power test; Regression equation

Indexed keywords

ANDERSON-DARLING TESTS; CRITICAL VALUE; EMPIRICAL DISTRIBUTION FUNCTIONS; EXTREME VALUE DISTRIBUTIONS; FREQUENCY ANALYSIS; GOODNESS-OF-FIT TEST; REGRESSION EQUATION; STATISTICAL RESEARCH;

COMPUTER SIMULATION; DISTRIBUTION FUNCTIONS; PROBABILITY DISTRIBUTIONS; REGRESSION ANALYSIS; STATISTICS;

STATISTICAL TESTS;

CRITICAL ANALYSIS; DATA SET; NUMERICAL MODEL; OBSERVATIONAL METHOD; PARAMETERIZATION; POPULATION STRUCTURE; STATISTICAL ANALYSIS;

EID: 84880605994     PISSN: 00221694     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jhydrol.2013.06.008     Document Type: Article

References (37)

1. Ahmad M.I., Sinclair C.D., Spurr B.D. Assessment of flood frequency models using empirical distribution function statistics. Water Resour. Res. 1988, 24(8):1323-1328.
2. Aho M., Bain L.J., Engelhardt M. Goodness-of-fit tests for the Weibull distribution with unknown parameters and heavy censoring. J. Stat. Comput. Simul. 1985, 21:213-225.
3. Anderson T.W., Darling D.A. Asymptotic theory of certain "goodness-of-fit" criteria based on stochastic processes. Ann. Math. Stat. 1952, 23:193-212.
4. Arshad M., Rasool M.T., Ahmad M.I. Anderson Darling and modified Anderson Darling tests for generalized Pareto distribution. Pakistan Journal of Applied Sciences 2003, 3(2):85-88.
5. Bush J.G., Woodruff B.W., Moore A.H., Dunne E.J. Modified Cramer von Mises and Anderson-Darling tests for Weibull distributions with unknown location and scale parameters. Communications in Statistics - Theory and Methods 1983, 12(21):2465-2476.
6. Chandra M., Singpurwalla N.D., Stephens M.A. Kolmogorov statistics for tests of fit the extreme value and Weibull distributions. Journal of the American Statistical Association 1981, 76(375):729-731.
7. Chowdhury J.U., Stedinger J.R., Lu L.H. Goodness-of-fit tests for regional generalized extreme value flood distributions. Water Resour. Res. 1991, 27(1):1765-1776.
8. Crown J.S. Percentage points for directional Anderson-Darling goodness-of-fit tests. Communication in Statistics-Simulation and Computation 2000, 29(2):523-532.
9. D'Agostino R.B., Stephens M.A. Goodness-of-Fit Techniques 1986, Marcel Dekker, New York.
10. Fill H.D., Stedinger J.R. L moment and probability plot correlation coefficient goodness-of-fit tests for the Gumbel distribution and impact of autocorrelation. Water Resour. Res. 1995, 31(1):225-229.
11. Filliben J.J. The probability plot correlation coefficient test for normality. Technometrics 1975, 17(1):111-117.
12. Green J.R., Hegazy Y.A.S. Powerful modified EDF goodness-of-fit tests. Journal of the American Statistical Association 1976, 71:204-209.
13. Heo J., Kho Y.W., Shin H., Kim S., Kim T. Regression equations of probability plot correlation coefficient test statistics from several probability distributions. J. Hydrol. 2008, 355:1-15.
14. Kolmogorov A. Grundbegriffe der Wahrscheinlichkeitsrechnung 1933, Julius Springer, Berlin.
15. Laio F. Cramer von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters. Water Resour. Res. 2004, 40:W09308.
16. Landwehr J.M., Matalas N.C. Estimation of parameters and quantiles of Wakeby distributions: 1. Known lower bounds. Water Resour. Res. 1979, 15(6):1361-1371.
17. Landwehr J.M., Matalas N.C. Estimation of parameters and quantiles of Wakeby distributions: 1. Unknown lower bounds. Water Resour. Res. 1979, 15(6):1372-1379.
18. Landwehr J.M., Matalas N.C. Quantile estimation with more or less floodlike distributions. Water Resour. Res. 1980, 16(3):547-555.
19. Legates D.R., McCabe G.J. Evaluating the use of "goodness-of-fit" measures in hydrologic and hydroclimatic model validation. Water Resour. Res. 1999, 35(1):233-241.
20. Liao, M., Shimokawa, T., 1999. Goodness-of-fit tests for the Type-I extreme-value and two-parameter Weibull distributions with unknown parameters estimated by graphical plotting techniques. National Aerospace Laboratory 1999 Part 2: Power study, Technical Report. TR-1372T.
21. Lilliefors H.W. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association 1967, 62:399-402.
22. Lilliefors H.W. On the Kolmogorov-Smirnov test for the exponential distribution with mean unknown. Journal of the American Statistical Association 1969, 64:387-389.
23. Looney S.W., Gulledge T.R.J. Use the correlation coefficient with normal probability plots. The American Statistician 1985, 39(1):75-79.
24. Onoz B., Bayazit M. Best-fit distributions of largest available flood samples. J. Hydrol. 1995, 167:195-208.
25. Pettitt A.N., Stephens M.A. Modified Cramer-von Mises statistics for censored data. Biometrika 1976, 63:291-298.
26. Porter J.E., Coleman J.W., Moore A.H. Modified KS, AD, and CvM tests for the Pareto distribution with unknown location and scale parameters. IEEE Trans. Reliab. 1992, 41(1):112-117.
27. Shimokawa T., Liao M. Goodness-of-fit tests for the type I extreme value and 2 parameter Weibull distributions. IEEE Trans. Reliab. 1999, 48(1):79-86.
28. Shin H., Jung Y., Jeong C., Heo J.H. Assessment of modified Anderson-Darling test statistics for the generalized extreme value and generalized logistic distributions. Stoch. Env. Res. Risk Assess. 2012, 26:105-114.
29. Sinclair C.D., Spurr B.D., Ahmad M.I. Modified Anderson Darling test. Commun. Stat. Theory Methods 1990, 19(10):3677-3686.
30. Song S., Singh V.P. Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data. Stoch. Env. Res. Risk Assess. 2010, 24:425-444.
31. Stephens M.A., ( Use of the Kolmogorov-Smirnov, Cramer von Mises and related statistics without extensive tables. Journal of the Royal Statistical Society, B 1970, (32):115-122.
32. Stephens M.A. EDF statistics for goodness of fit and some comparisons. J. Am. Stat. Assoc. 1974, 69:730-737.
33. Stephens, M.A., 1976. Asymptotic Power of EDF Statistics for Exponentiality Against Gamma and Weibull Alternatives. Tech Report No. 297, Dept. Stat. Stanford Univ.
34. Sultan A.M., Khaleel H.M. A new modified goodness of fit tests for type 2 censored sample from normal population. Math. Comput. Appl. 2005, 10(2):165-177.
35. Tolikas K., Heravi S. The Anderson-Darling goodness-of-fit test statistic for the three-parameter lognormal distribution. Commun. Stat. Theory Methods 2008, 37:3135-3143.
36. Vogel R.W., McMartin D.E. Probability plot goodness-of-fit and skewness estimation procedures for the Pearson type 3 distribution. Water Resour. Res. 1991, 27(12). 10.1029/91WR02116.
37. Wang Q.J. Approximate goodness-of-fit tests of fitted generalized extreme value distribution using LH moments. Water Resour. Res. 1998, 34(12):3494-3502.