Monte Carlo comparison of goodness-of-fit tests for the Inverse Gaussian distribution based on empirical distribution function

Document Type : Research Paper

Authors

1 Department of Statistics, University of Birjand, Birjand, Iran

2 Department of Mathematics and Statistics, University of Gonabad, Gonabad, Iran

Abstract

The Inverse Gaussian (IG) distribution is widely used to model positively skewed data. In this article, we examine goodness of fit tests for the Inverse Gaussian distribution based on the empirical distribution function. In order to compute the test statistics, parameters of the Inverse Gaussian distribution are estimated by maximum likelihood estimators (MLEs), which are simple explicit estimators. Critical points and the actual sizes of the tests are obtained by Monte Carlo simulation. Through a simulation study, power values of the tests are compared with each other. Finally, an illustrative example is presented and analyzed.

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References

1] Allison, J.S., Betsch, S., Ebner, B., and Visagie, J. (2022), On testing the adequacy of the inverse Gaussian distribution, Mathematics, 10, 350.
[2] Al-Omari, A.I. and Haq, A. (2016), Entropy estimation and goodness-of- t tests for the inverse Gaussian and Laplace distributions using paired ranked set sampling, Journal of Statistical Computation and Simulation, 86, 2262-2272.
[3] Anderson, T.W. and Darling, D.A. (1954), A test of goodness of  t, Journal of American Statistical Association, 49, 765-769.
[4] Bardsley, W.E. (1980), Note on the use of the inverse Gaussian distribution for wind energy applications, Journal of Applied Meteorology, 19, 1126{1130.
[5] Barndor -Nielsen, O.E. (1994), A note on electrical networks and the inverse Gaussian distribution, Advances in Applied Probability, 26, 63{67.
[6] Chen, Z. (2000), A new two-parameter lifetime distribution with bathtub shape or increasing failure note function, Statistics and Probability Letters, 49, 155{161.
[7] D'Agostino, R.B. and Stephens, M.A. (Eds.) (1986), Goodness-of- t Techniques, New York: Marcel Dekker.
[8] Dhillon, B.S. (1981), Lifetime Distributions, IEEE Transactions on Reliability, 30 457{459.
[9] Folks, J.L. and Chhikara, R.S. (1978), The inverse Gaussian distribution and its statistical application-a review, Journal of the Royal Statistical Society of Great Britain, 40, 263{289.
[10] Folks, J.L. and Chhikara, R.S. (1989), In: The Inverse Gaussian Distribution, Theory, Methodology and Applications. Marcel Dekker, New York.
[11] Gunes, H., Dietz, D.C., Auclair, P.F., and Moore, A.H. (1997), Modi ed goodness-of- t tests for the inverse Gaussian distribution, Computational statistics & Data analysis, 24, 63-77.
[12] Henze, N., and Klar, B. (2002), Goodness-of- t tests for the inverse Gaussian distribution based on the empirical Laplace transform, Annals of the Institute of Statistical Mathematics, 54, 425-444.
[13] Huber-Carol, C., Balakrishnan, N., Nikulin, M. S. and Mesbah, M. (2002), Goodnessof- t tests and model validity, Boston, Basel, Berlin: Birkhauser.
[14] Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994), Continuous Univariate Distributions, 1 and 2, Wiley, New York.
[15] Kolmogorov, A.N. (1933), Sulla Determinazione Empirica di une legge di Distribuzione. Giornale dell'Intituto Italiano degli Attuari, 4, 83-91.
[16] Kuiper, N.H. (1960), Tests concerning random points on a circle, Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, Series A, 63, 38-47.
[17] Ofosuhene, P. (2020), The energy goodness-of- t test for the inverse Gaussian distribution (Doctoral dissertation, Bowling Green State University).
[18] O'Reilly, F.J. and Rueda, R. (1992), Goodness of  t for the inverse Gaussian distribution, Canadian Journal of Statistics, 20, 387-397.
[19] Seshadri, V. (1999), In: The Inverse Gaussian Distribution: Statistical Theory and Applications, Springer, New York.
[20] Torabi, H., Montazeri, N.H. and Grane, A. (2016), A test for normality based on the empirical distribution function, SORT, 40, 55-88.
[21] Torabi, H., Montazeri, N.H. and Grane, A. (2018), A wide review on exponentiality tests and two competitive proposals with application on reliability, Journal of Statistical Computation and Simulation, 88, 108-139.
[22] von Mises, R. (1931), Wahrscheinlichkeitsrechnung und ihre Anwendung in der Statistik und theoretischen Physik, Leipzig and Vienna: Deuticke.
[23] Watson, G.S. (1961), Goodness of  t tests on a circle, Biometrika, 48, 109-114.
[24] Zhang, J. (2002), Powerful goodness-of- t tests based on the likelihood ratio, Journal of Royal Statistical Society, Series B, 64, 281-294.

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History

  • Receive Date: 14 January 2023
  • Revise Date: 14 April 2023
  • Accept Date: 15 April 2023

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