A comparison of uniformity tests

Statistics

Volumn 39, Issue 4, 2005, Pages 315-327

  Marhuenda, Y ^a   Morales, D ^a   Pardo, M C ^b  

^a MIGUEL HERNÁNDEZ UNIVERSITY   (Spain)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Inefficiency; Monte carlo simulation; Power; Uniformity tests

Indexed keywords

EID: 23744489680     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331880500178562     Document Type: Article

References (46)

1. Kolmogorov, A.N., 1933, Sulla determinazione empirica di una legge di distibuziane. Giornale dell'Istituta Italiano degli Attuari, 4, 83-91.
2. Kuiper, N.H., 1960, Tests concerning random points on a circle. Proceedings of the Koninklijke Nederlondse Akademie van Wetenschappen Series A, 63, 38-47.
3. N: distribution and significance points. Biometrika, 52, 309-321.
4. Anderson, T.W. and Darling, D.A., 1954, A test of goodness-of-fit. Journal of the American Statistical Association, 49, 765-769.
5. Lewis, P.A.W., 1961, Distribution of the Anderson-Darling statistic. Annals of Mathematical Statistics, 32, 1118-1124.
6. Watson, G.S., 1961, Goodness-of-fit on a circle. Biometrika, 48, 109-114.
7. Durbin, J., 1969, Test for serial correlation in regression analysis based on the periodogram of least-squares residuals. Biometrika, 56, 1-16.
8. Brunk, H.D., 1962, On the range of the difference between hypothetical distribution function and Pyke's modified empirical distribution function. Annals of Mathematical Statistics, 33, 525-532.
9. Stephens, M. A., 1969, Results from the relation between two statistics of the Kolgomorov-Smirnov type. Annals of Mathematical Statistics, 40, 1833-1837.
10. Hegazy, Y.A.S. and Green, J.R., 1975, Some new goodness-of-fit tests using order statistics. Applied Statistics, 24, 299-308.
11. D'Agostino, R.B. and Stephens, M.A., 1986, Goodness-of-Fit Techniques, Statistics, Textbook and Monographs, Vol. 68 (New York: Marcel Dekker, Inc.).
12. Greenwood, M., 1946, The statistical study of infectious diseases. Journal of Royal Statistical Society Series A, 109, 85-110.
13. Moran, P.A.P., 1947, The random division of an interval - Part I. Journal of Royal Statistical Society Series B, 9, 92-98.
14. Moran, P.A.P., 1951, The random division of an interval - Part II. Journal of Royal Statistical Society Series B, 13, 147-150.
15. Burrows, P.M., 1979, Selected percentage points of Greenwood's statistic. Journal of Royal Statistical Society, 142, 256-258.
16. Hill, I.D., 1979, Approximating the distribution of Greenwood's statistic with Johnson distributions. Journal of Royal Statistical Society Series A, 142, 378-380. (Corrigendum (1981). Journal of Royal Statistical Society Series A, 144, 388).
17. Currie, I.D., 1981, Further percentage points for Greenwood's Statistic. Journal of Royal Statistical Society Series A, 144, 360-363.
18. Stephens, M.A., 1981, Further percentage points for Greenwood's statistic. Journal of Royal Statistical Society Series A, 144, 364-366.
19. Quesenberry, C.P. and Miller, F.L. Jr., 1977, Power studies of some tests for uniformity. Journal of Statistical Computation and Simulation, 5, 169-191.
20. Read, R.C. and Cressie, N.A.C., 1988, Goodness-of-fit Statistics for Discrete Multivariate Data (New York: Springer Verlag).
21. Darling, D. A., 1953, On a class of problems related to the random division of an interval. Annals of Mathematical Statistics, 24, 239-253.
22. Gebert, J.R. and Kale, B.K., 1969, Goodness of fit tests based on discriminatory information. Statistische Hefte, 10, 192-200.
23. Del Pino, G.E., 1979, On the asymptotic distribution of k-spacing with applications to goodness-of-fit tests. Annals of Statistics, 7, 1058-1065.
24. Hartley, H.O. and Pfaffenberger, R.C., 1972, Quadratic forms in order statistics used as goodness-of-fit criteria. Biometrika, 59, 605-611.
25. Cressie, N., 1976, On the logarithms of high order spacings. Biometrika, 63, 343-355.
26. Cressie, N., 1977, The minimum of higher order gaps. Australian Journal of Statistics, 19, 132-143.
27. Cressie, N., 1978, Power results for tests based on high order gaps. Biometrika, 65, 214-218.
28. Cressie, N., 1979, An optimal statistic based on higher order gaps. Biometrika, 66, 619-627.
29. Deken, J.G., 1980, Exact distributions for gaps and stretches. Technical Report, Department of Statistics, Stanford University.
30. McLaren, C.G. and Stephens, M.A., 1985, Percentage points and power for spacings statistics for testing uniformity. Technical Report, Department of Mathematics and Statistics, Simon Fraser University.
31. Vasicek, O., 1976, A test for normality based on sample entropy. Journal of the Royal Statistical Society Series B, 38, 54-59.
32. Dudewicz, E.J. and van der Meulen, E.C., 1981, Entropy-based tests of uniformity. Journal of the American Statistical Association, 76, 967-974.
33. Swartz, T., 1992, Goodness-of-fit tests using Kullback-Leibler information. Communications in Statistics. Theory and Methods, 21, 711-729.
34. Stephens, M.A., 1974, EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730-737.
35. Morales, D., Pardo, L., Pardo, M.C. and Vajda, I., 2003, Limit laws for disparities of spacings. Journal of Nonparametric Statistics, 15(3), 325-342.
36. Pardo, M.C., 2003, A test for uniformity based on informational energy. Statistical Papers, 44, 521-534.
37. Cressie, N. and Read, T.R.C., 1984, Multinomial goodness-of-fit tests. Journal of the Royal Statistic Society Series B, 46, 440-464.
38. Marhuenda, M.A., Marhuenda, Y. and Morales, D., 2005a, Uniformity tests under quantite categorization. Kybernetes (in press Vol. 34, number 5/6).
39. Neyman, J., 1937, Smooth test for goodness of fit. Skandinavisk Aktuarietidskrift, 20, 150-199.
40. Ledwina, T., 1994, Data-driven version of Neyman's smooth test of fit. Journal of the American Statistical Association, 89, 1000-1005.
41. Schwarz, G., 1978, Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
42. Zhang, J., 2002, Powerful goodness-of-fit tests based on the likelihood ratio. Journal of Royal Statistical Society Series B, 64, 281-294.
43. Wichmann, B.A. and Hill, I.D., 1982, Algorithm AS 183: An efficient and portable pseudo-random number generator. Applied Statistics, 31, 188-190 (Corrections (1984). Applied Statistics, 33, 123).
44. Marhuenda, Y., 2002, Contrastes de uniformidad. PhD thesis, Miguel Hernández University, Spain.
45. Marhuenda, Y., Morales, D. and Pardo, M.C., 2005, Power results of tests for the uniform distribution. Technical Report (I-2005-09), Operation Research Center, Miguel Hernández University of Elche (Spain).
46. Stephens, M.A., 1970, Use of the Kolgomorov-Smirnov, Cramer-von Mises and related statistics without extensive tables. Journal of Royal Statistical Society Series B, 32, 115-122.