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Modified goodness-of-fit tests for the inverse Gaussian distribution. (English) Zbl 0900.62231

Summary: Modified Kolmogorov–Smirnov (KS), Kuiper (V), Cramer–von Mises (CV), Watson (W), Anderson–Darling (AD) and sequential goodness-of-fit tests are developed for the inverse Gaussian distribution with unknown parameters. A Monte Carlo procedure is employed to generate critical values for a wide range of sample sizes and shape parameters. Power studies indicate that the W test is most effective against alternate distributions that are very similar in shape to the null inverse Gaussian distribution. Otherwise, the modified AD test generally demonstrates the highest power among single tests. To eliminate the need for extensive critical value tables, functional relationships between critical values, sample sizes, and shape parameters are reported.

MSC:

62G10 Nonparametric hypothesis testing
65C99 Probabilistic methods, stochastic differential equations
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[1] Chen, G.; Balakrishnan, N.: A general purpose approximate goodness-of-fit test. J. quality technol. 27, 154-161 (1995)
[2] Chhikara, R. S.; Folks, J. L.: The inverse Gaussian distribution as a lifetime model. Technometrics 19, 461-468 (1977) · Zbl 0372.62076
[3] Chhikara, R. S.; Folks, J. L.: The inverse Gaussian distribution: theory, methodology, and applications. (1989) · Zbl 0701.62009
[4] Daniel, W. W.: Goodness-of-fit: A selected bibliography for the statistician and researcher. Public administration series: bibliography, vance bibliographies (1980)
[5] David, F. N.; Johnson, N. L.: The probability integral transformation when parameters are estimated from the sample. Biometrika 35, 182-190 (1948) · Zbl 0030.40503
[6] Edgeman, R. L.; Scott, R. C.; Pavur, R. J.: A modified Kolmogorov-Smirnov test for the inverse Gaussian density with unknown parameters. Comm. statist. Simulation 17, 1203-1212 (1988) · Zbl 0695.62116
[7] Folks, J. L.; Chhikara, R. S.: The inverse Gaussian distribution and its statistical application – a review. J. roy. Statist. soc. 40, 263-289 (1978) · Zbl 0408.62011
[8] Jr., M. C. Gacula; Kubala, J. J.: Statistical models for shelf life failures. J. food sci. 40, 404-409 (1975)
[9] Harter, H. L.: Another look at plotting positions. Comm. statist. 14, No. 2, 317-343 (1985)
[10] Johnson, N. L.; Kotz, S.; Balakrishnan, N.: Distributions in statistics – continuous univariate distributions. (1994) · Zbl 0811.62001
[11] Michael, J. R.; Schucany, W.; Haas, R.: Generating random variates using transformations with multiple roots. Amer. statist. 30, 87-90 (1976) · Zbl 0331.65002
[12] O’reilly, F. J.; Rueda, R.: Goodness of fit for the inverse Gaussian distribution. Canad. J. Statist. 20, 387-397 (1992) · Zbl 0765.62051
[13] Pavur, R. J.; Edgeman, R. L.; Scott, R. C.: Quadratic statistics for the goodness-of-fit test of the inverse Gaussian distribution. IEEE trans. Reliab. 41, 118-123 (1992) · Zbl 0800.62614
[14] Seshadri, V.: The inverse guassian distribution: A case study in exponential families. (1994)
[15] Shuster, J. J.: On the inverse guassian distribution function. J. amer. Statist. assoc. 63, 1514-1516 (1968) · Zbl 0169.21004
[16] Stephens, M. A.; D’agostino, R. B.: Goodness-of-fit techniques. (1986) · Zbl 0597.62030
[17] Tweedie, M. C. K.: Statistical properties of the inverse Gaussian distribution I. Ann. math. Statist. 28, 362-377 (1957) · Zbl 0086.35202
[18] Von Alven, W. H.: Reliability engineering by ARINC. (1964)
[19] Wasan, M. T.: Sufficient conditions for a first passage time process to be that of Brownian motion. Appl. probab. 6, 218-223 (1969) · Zbl 0184.21204
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