Goodness-of-fit tests for the inverse Gaussian distribution based on the empirical Laplace transform

Annals of the Institute of Statistical Mathematics

Volumn 54, Issue 2, 2002, Pages 425-444

  Henze, Norbert ^a   Klar, Bernhard ^a  

^a UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Empirical Laplace transform; Goodness of fit test; Inverse Gaussian distribution; Parametric bootstrap; Smooth tests of fit

Indexed keywords

COMPUTER SIMULATION; LAPLACE TRANSFORMS; PROBABILITY DISTRIBUTIONS;

INVERSE GAUSSIAN DISTRIBUTION;

STATISTICAL TESTS;

EID: 6444245797     PISSN: 00203157     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022442506681     Document Type: Article

References (31)

1. Baringhaus, L., Gürtler, N., and Henze, N. (2000). Weighted integral tests of fit, Australian & New Zealand Journal of Statistics, 42(2), 179-192.
2. Baringhaus, L. and Henze, N. (1991). A class of consistent tests for exponentiality based on the empirical Laplace transform, Ann. Inst. Statist. Math., 43, 551-564.
3. Baringhaus, L. and Henze, N. (1992). A goodness of fit test for the Poisson distribution based on the empirical generating function, Statist. Prob. Lett., 13, 269-274.
4. Bhattacharyya, G. and Fries, A. (1982). Fatigue failure models - Birnbaum-Saunders vs. inverse Gaussian, IEEE Trans. Reliab., R-31, 439-441.
5. Billingsley, P. (1968). Convergence of Probability Measures, Wiley, New York.
6. Chhikara, R. Folks, J. (1977). The inverse Gaussian distribution as a lifetime model, Technometrics, 19, 461-468.
7. Chhikara, R. and Folks, J. (1989). The Inverse Gaussian Distribution, Theory, Methodology and Applications, Marcel, New York.
8. Courant, R. and Hilbert, D. (1953). Methods of Mathematical Physics, VOL I, Interscience, New York.
9. Edgeman, R., Scott, R. and Pavur, R. (1988). A modified Kolmogorov-Smirnov test for the inverse Gaussian density with unknown parameters, Comm. Statist. Simulation Comput., 17, 1203-1212.
10. Epps, T. (1995). A test of fit for lattice distributions, Comm. Statist. Theory Methods, 24(6), 1455-1479.
11. Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. II, 2nd ed., Wiley, New York.
12. Gunes, H., Dietz, D., Auclair, P. and Moore, A. (1997). Modified goodness-of-fit tests for the inverse Gaussian distribution, Comput. Statist. Data Anal., 24, 63-77.
13. Gürtler, N. and Henze, N. (2000). Recent and classical goodness-of-fit tests for the Poisson distribution, J. Statist. Plann. Inference, 90, 207-225.
14. Henze, N. (1993). A new flexible class of omnibus tests for exponentiality, Comm. Statist. Theory Methods, 22, 115-133.
15. Henze, N. (1996). Empirical-distribution-function goodness-of-fit tests for discrete models, Canad. J. Statist., 24(1), 81-93.
16. Henze, N. and Meintanis, S. (2000). Tests of fit for exponentiality based on the empirical Laplace transform, Statistics (to appear).
17. Henze, N. and Wagner, T. (1997). A new approach to the BHEP tests for multivariate normality, J. Multivariate Anal., 62(1), 1-23.
18. Hougaard, P. (1984). Life table methods for heterogeneous populations: Distributions describing the heterogeneity, Biometrika, 71, 75-83.
19. Klar, B. (2000). Diagnostic smooth tests of fit, Metrika, 52, 237-252.
20. Kundu, S., Majumdar, S. and Mukherjee, K. (2000). Central limit theorems revisited, Statist. Probab. Lett., 47, 265-275.
21. Mergel, V. (1999). Test of goodness of fit for the inverse-gaussian distribution, Math. Commun., 4, 191-195.
22. Michael, J., Schucancy, W. and Haas, R. (1976). Generating random variates using transformations with multiple roots, Amer. Statist., 30(2), 88-90.
23. Nakamura, M. and Pérez-Abreu, V. (1993). Use of an empirical probability generating function for testing a Poisson model, Canad. J. Statist., 21(2), 149-156.
24. O'Reilly, F. and Rueda, R. (1992). Goodness of fit for the inverse Gaussian distribution, Canad. J. Statist., 20, 387-397.
25. Padgett, W. and Tsoi, S. (1986). Prediction intervals for future observations from the inverse Gaussian distribution, IEEE Trans. Reliab., R35, 406-408.
26. Pavur, R., Edgeman, R. and Scott, R. (1992). Quadratic statistics for the goodness-of-fit test of the inverse Gaussian distribution, IEEE Trans. Reliab., 41, 118-123.
27. Rueda, R. and O'Reilly, F. (1999). Tests of fit for discrete distributions based on the probability generating function, Commun. Statist. Simulation Comput, 28(1), 259-274.
28. Seshadri, V. (1993). The Inverse Gaussian Distribution - A Case Study in Exponential Families, Clarendon Press, Oxford.
29. Seshadri, V. (1999). The Inverse Gaussian Distribution - Statistical Theory and Applications, Springer, New York.
30. Stute, W., Manteiga, W. and Quindimil, M. (1993). Bootstrap based goodness-of-fit tests, Metrika, 40, 243-256.
31. Widder, D. (1959). The Laplace Transform, 5th ed., Princeton University Press, New Jersey.