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

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  • Hadi Alizadeh Noughabi
  • Albert Vexler

Abstract

The inverse Gaussian (IG) distribution is widely used to model positively skewed data. An important issue is to develop a powerful goodness-of-fit test for the IG distribution. We propose and examine novel test statistics for testing the IG goodness of fit based on the density-based empirical likelihood (EL) ratio concept. To construct the test statistics, we use a new approach that employs a method of the minimization of the discrimination information loss estimator to minimize Kullback–Leibler type information. The proposed tests are shown to be consistent against wide classes of alternatives. We show that the density-based EL ratio tests are more powerful than the corresponding classical goodness-of-fit tests. The practical efficiency of the tests is illustrated by using real data examples.

Suggested Citation

  • Hadi Alizadeh Noughabi & Albert Vexler, 2016. "An efficient correction to the density-based empirical likelihood ratio goodness-of-fit test for the inverse Gaussian distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2988-3003, December.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:16:p:2988-3003
    DOI: 10.1080/02664763.2016.1156657
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    References listed on IDEAS

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    1. Albert Vexler & Young Min Kim & Jihnhee Yu & Nicole A. Lazar & Alan D. Hutson, 2014. "Computing Critical Values of Exact Tests by Incorporating Monte Carlo Simulations Combined with Statistical Tables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1013-1030, December.
    2. Miecznikowski, Jeffrey & Vexler, Albert & Shepherd, Lori, 2013. "dbEmpLikeGOF: An R Package for Nonparametric Likelihood Ratio Tests for Goodness-of-Fit and Two-Sample Comparisons Based on Sample Entropy," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 54(i03).
    3. Albert Vexler & Jihnhee Yu & Alan D. Hutson, 2011. "Likelihood testing populations modeled by autoregressive process subject to the limit of detection in applications to longitudinal biomedical data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1333-1346, May.
    4. Vexler, Albert & Gurevich, Gregory, 2010. "Empirical likelihood ratios applied to goodness-of-fit tests based on sample entropy," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 531-545, February.
    5. Albert Vexler & Wan-Min Tsai & Alan D. Hutson, 2014. "A Simple Density-Based Empirical Likelihood Ratio Test for Independence," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 158-169, February.
    6. Soofi, E. S. & Retzer, J. J., 2002. "Information indices: unification and applications," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 17-40, March.
    7. Wan-Min Tsai & Albert Vexler & Gregory Gurevich, 2013. "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 a," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(6), pages 1189-1208, June.
    8. Ebrahimi, Nader & Pflughoeft, Kurt & Soofi, Ehsan S., 1994. "Two measures of sample entropy," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 225-234, June.
    9. Albert Vexler & Shuling Liu & Enrique F. Schisterman, 2011. "Nonparametric-likelihood inference based on cost-effectively-sampled-data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 769-783, February.
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