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Original Articles

An efficient correction to the density-based empirical likelihood ratio goodness-of-fit test for the inverse Gaussian distribution

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Pages 2988-3003 | Received 27 Jan 2015, Accepted 17 Feb 2016, Published online: 23 Mar 2016

References

  • H. Alizadeh Noughabi and N.R. Arghami, Goodness-of-fit tests based on correcting moments of entropy estimators, Commun. Stat. Simul. Comput. 42 (2013), pp. 499–513. doi: 10.1080/03610918.2011.634535
  • A. Ang and W.H. Tang, Probability Concepts in Engineering Planning and Design, Vol. I, Wiley, New York, 1975.
  • W.E. Bardsley, Note on the use of the inverse Gaussian distribution for wind energy applications, J. Appl. Meteorol. 19 (1980), pp. 1126–1130. doi: 10.1175/1520-0450(1980)019<1126:NOTUOT>2.0.CO;2
  • O.E. Barndorff-Nielsen, A note on electrical networks and the inverse Gaussian distribution, Adv. Appl. Probab. 26 (1994), pp. 63–67. doi: 10.2307/1427579
  • N. Ebrahimi, K. Pflughoeft, and E. Soofi, Two measures of sample entropy, Stat. Probab. Lett. 20 (1994), pp. 225–234. doi: 10.1016/0167-7152(94)90046-9
  • R.L. Edgeman, Assessing the inverse Gaussian distribution assumption, IEEE Trans. Reliab. 39 (1990), pp. 352–355. doi: 10.1109/24.103017
  • R.L. Edgeman, R.C. Scott, and R.J. Pavur, A modified Kolmogorov–Smirnov test for the inverse Gaussian density with unknown parameters, Commun. Stat. Simul. Comput. 17 (1988), pp. 1203–1212. doi: 10.1080/03610918808812721
  • J.L. Folks and R.S. Chhikara, The inverse Gaussian distribution and its statistical application – A review, J. R. Stat. Soc. Great Britain 40 (1978), pp. 263–289.
  • J.L. Folks and R.S. Chhikara, The Inverse Gaussian Distribution, Theory, Methodology and Applications, Marcel Dekker, New York, 1989.
  • G. Gurevich and A. Vexler, A two-sample empirical likelihood ratio test based on samples entropy, Stat. Comput. 21 (2011), pp. 657–670. doi: 10.1007/s11222-010-9199-7
  • N.L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Vols. 1 and 2, Wiley, New York, 1994.
  • J.C. Miecznikowski, A. Vexler, and L. Shepherd, dbEmpLikeGOF: An R package for nonparametric likelihood ratio tests for goodness-of-fit and two-sample comparisons based on sample entropy, J. Stat. Softw. 54 (2013), pp. 1–19. doi: 10.18637/jss.v054.i03
  • G.S. Mudholkar, R. Natarajan, and Y.P. Chaubey, A goodness-of-fit test for the inverse Gaussian distribution using its independence characterization, Sankhya B 63 (2001), pp. 362–374.
  • G.S. Mudholkar and L. Tian, An entropy characterization of the inverse Gaussian distribution and related goodness-of-fit test, J. Stat. Plan. Inference 102 (2002), pp. 211–221. doi: 10.1016/S0378-3758(01)00099-4
  • A.B. Owen, Empirical Likelihood, Chapman and Hall, New York, 2001.
  • S. Park and D. Park, Correcting moments for goodness of fit tests based on two entropy estimates, J. Stat. Comput. Simul. 73 (2003), pp. 685–694. doi: 10.1080/0094965031000070367
  • V. Seshadri, The Inverse Gaussian Distribution: A Case Study in Exponential Families, Clarendon Press, Oxford, 1993.
  • V. Seshadri, The Inverse Gaussian Distribution: Statistical Theory and Applications, Springer, New York, 1999.
  • L.A. Shepherd, W.-M. Tsai, A. Vexler, and J.C. Miecznikowski, dbEmpLikeNorm: Test for Joint Assessment of Normality, R Package, 2013. Available at http://cran.r-project.org/web/packages/dbEmpLikeNorm/index.html.
  • E.S. Soofi, Principal information theoretic approaches, J. Am. Stat. Assoc. 95 (2000), pp. 1349–1353. doi: 10.1080/01621459.2000.10474346
  • E.S. Soofi, N. Ebrahimi, and M. Habibullah, Information distinguishability with application to analysis of failure data, J. Am. Stat. Assoc. 90 (1995), pp. 657–668. doi: 10.1080/01621459.1995.10476560
  • E.S. Soofi and J.J. Retzer, Information indices: Unification and applications, J. Econ. 107 (2002), pp. 17–40. doi: 10.1016/S0304-4076(01)00111-7
  • H. Tanajian, A. Vexler, and A.D. Hutson, Novel and Efficient Density Based Empirical Likelihood Procedures for Symmetry and K-Sample Comparisons: STATA Package, 2013. Available at http://sphhp.buffalo.edu/biostatistics/research-and-facilities/software/stata.html.
  • W.-M. Tsai, A. Vexler, and G. Gurevich, An extensive power evaluation of a novel two-sample density-based empirical likelihood ratio test for paired data with an application to a treatment study of attention-deficit/hyperactivity disorder and severe mood dysregulation, J. Appl. Stat. 40 (2013), pp. 1189–1208. doi: 10.1080/02664763.2013.784895
  • O. Vasicek, A test for normality based on sample entropy, J. R. Stat. Soc. Ser. B 38 (1976), pp. 54–59.
  • A. Vexler and G. Gurevich, Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy, Comput. Stat. Data Anal. 54 (2010), pp. 531–545. doi: 10.1016/j.csda.2009.09.025
  • A. Vexler and G. Gurevich, A note on optimality of hypothesis testing, Math. Eng. Sci. Aerospace 2 (2011), pp. 243–250.
  • A. Vexler, Y.M. Kim, J. Yu, N.A. Lazar, and A.D. Hutson, Computing critical values of exact tests by incorporating Monte Carlo simulations combined with statistical tables, Scand. J. Stat. 41 (2014), pp. 1013–1030. doi: 10.1111/sjos.12079
  • A. Vexler, S. Liu, and E.F. Schisterman, Nonparametric likelihood inference based on cost-effectively-sampled-data, J. Appl. Stat. 38 (2011), pp. 769–783. doi: 10.1080/02664761003692290
  • A. Vexler, G. Shan, S. Kim, W.M. Tsai, L. Tian, and A.D. Hutson, An empirical likelihood ratio based goodness-of-fit test for Inverse Gaussian distributions, J. Stat. Plan. Inference 141 (2011), pp. 2128–2140. doi: 10.1016/j.jspi.2010.12.024
  • A. Vexler, W.-M. Tsai, G. Gurevich, and J. Yu, Two-sample density-based empirical likelihood ratio tests based on paired data, with application to a treatment study of attention-deficit/hyperactivity disorder and severe mood dysregulation, Stat. Med. 31 (2012), pp. 1821–1837. doi: 10.1002/sim.4467
  • A. Vexler, W.-M. Tsai, and A.D. Hutson, A simple density-based empirical likelihood ratio test for Independence, Am. Stat. 68 (2014), pp. 158–169. doi: 10.1080/00031305.2014.901922
  • A. Vexler, W.-M. Tsai, and Y. Malinovsky, Estimation and testing based on data subject to measurement errors: From parametric to non-parametric likelihood methods, Stat. Med. 31 (2012), pp. 2498–2512. doi: 10.1002/sim.4304
  • A. Vexler and J. Yu, Two-sample density-based empirical likelihood tests for incomplete data in application to a pneumonia study, Biom. J. 53 (2011), pp. 628–651. doi: 10.1002/bimj.201000235
  • A. Vexler, J. Yu, and A.D. Hutson, Likelihood testing populations modeled by autoregressive process subject to the limit of detection in applications to longitudinal biomedical data, J. Appl. Stat. 38 (2011), pp. 1333–1346. doi: 10.1080/02664763.2010.498505

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