Tests of fit for the Gumbel distribution: EDF-based tests against entropy-based tests

References

• H. Alizadeh Noughabi, A new estimator of entropy and its application in testing normality. J. Stat. Comput. Simul. 80 (2010), pp. 1151–1162. doi: 10.1080/00949650903005656
   Web of Science ®Google Scholar
• H. Alizadeh Noughabi, and N.R. Arghami, Monte Carlo comparison of five exponentiality tests using different entropy estimates. J. Stat. Comput. Simul. 81 (2011), pp. 1579–1592. doi: 10.1080/00949655.2010.496368
   Web of Science ®Google Scholar
• H. Alizadeh Noughabi, and N.R. Arghami, General treatment of goodness of fit tests based on Kullback–Leibler information. J. Stat. Comput. Simul. 83 (2013), pp. 1556–1569. doi: 10.1080/00949655.2012.667100
   Web of Science ®Google Scholar
• R. Alizadeh Noughabi, H. Alizadeh Noughabi, and A. Ebrahimi Moghaddam Behabadi, An entropy test for the Rayleigh distribution and power comparison. J. Stat. Comput. Simul. 84 (2014), pp. 151–158. doi: 10.1080/00949655.2012.698620
   Web of Science ®Google Scholar
• E.H. Arruda, and P.M. Bentler, A regularized GLS for structural equation modeling. Struct. Equation Model.: Multi. J. 24 (2017), pp. 657–665. doi: 10.1080/10705511.2017.1318392
   Web of Science ®Google Scholar
• N. Balakrishnan, A. Habibi Rad, and N.R. Arghami, Testing exponentiality based on Kullback–Leibler information with progressively type-II censored data. IEEE Trans. Reliab. 56 (2007), pp. 301–307. doi: 10.1109/TR.2007.895308
   Web of Science ®Google Scholar
• B. Choi, K. Kim, and S. Heun Song, Goodness of fit test for exponentiality based on Kullback–Leibler information. Commun. Stat. Simul. Comput. 33 (2004), pp. 525–536. doi: 10.1081/SAC-120037250
   Web of Science ®Google Scholar
• J.C. Correa, A new estimator of entropy. Commun. Stat. Theory Methods 24 (1995), pp. 2439–2449. doi: 10.1080/03610929508831626
   Web of Science ®Google Scholar
• N. Ebrahimi, M. Habibullah, and E.S. Soofi, Testing exponentiality based on Kullback–Leibler information. J. Royal Stat. Soc., Ser B 54 (1992), pp. 739–748.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• M.D. Esteban, M.E. Castellanos, D. Morales, and I. Vajda, Monte Carlo comparison of four normality tests using different entropy estimates. Commun. Stat. Simul. Comput. 30 (2001), pp. 761–785. doi: 10.1081/SAC-100107780
   Web of Science ®Google Scholar
• A. Habibi Rad, F. Yousefzadeh, and N. Balakrishnan, Goodness-of-fit test based on Kullback–Leibler information for progressively type-II censored data. IEEE Trans. Reliab. 60 (2011), pp. 570–579. doi: 10.1109/TR.2011.2162470
   Web of Science ®Google Scholar
• W. Herzog, and A. Boomsma, Small-sample robust estimators of noncentrality based and incremental model fit. Struct. Equation Model.: Multi. J. 16 (2009), pp. 1–27. doi: 10.1080/10705510802561279
   Web of Science ®Google Scholar
• Y. Huang, and P.M. Bentler, Behavior of asymptotically distribution free test statistics in covariance versus correlation structure analysis. Struct. Equation Model.: Multi. J. 22 (2015), pp. 489–503. doi: 10.1080/10705511.2014.954078
   Web of Science ®Google Scholar
• S. Jalal, and P.M. Bentler, Using Monte Carlo normal distributions to evaluate structural models with nonnormal data. Struct. Equation Model. A Multi. J. (2017). doi:10.1080/10705511.2017.1390753.
   Web of Science ®Google Scholar
• G. Jiang, and K.H. Yuan, Four new corrected statistics for SEM with small samples and nonnormally distributed data. Struct. Equation Model. A Multi. J. 24 (2017), pp. 479–494. doi: 10.1080/10705511.2016.1277726
   Web of Science ®Google Scholar
• W.Q. Meeker, and L.A. Escobar, Statistical Methods for Reliability Data, John Wiley & Sons, Inc., New York, 1998.
   Google Scholar
• H. Noughabi, and R. Noughabi, On the entropy estimators. J. Stat. Comput. Simul. 83 (2013), pp. 784–792. doi: 10.1080/00949655.2011.637039
   Web of Science ®Google Scholar
• S. Park, Testing exponentiality based on the Kullback–Leibler information. IEEE Trans. Reliab. 54 (2005), pp. 22–26. doi: 10.1109/TR.2004.837314
   Web of Science ®Google Scholar
• P. Pérez-Rodríguez, H. Vaquera-Huerta, and J.A. Villaseñor-Alva, A goodness-of-fit test for the Gumbel distribution based on Kullback–Leibler information. Commun. Stat. Theory Methods 38 (2009), pp. 842–855. doi: 10.1080/03610920802316658
   Web of Science ®Google Scholar
• X. Tong, and P.M. Bentler, Evaluation of a new mean scaled and moment adjusted test statistic for SEM. Struct. Equation Model.: Multi. J. 20 (2013), pp. 148–156. doi: 10.1080/10705511.2013.742403
   PubMed Web of Science ®Google Scholar
• B. van Es, Estimating functionals related to a density by class of statistics based on spacings. Scand. J. Stat. 19 (1992), pp. 61–72.
   Web of Science ®Google Scholar
• O. Vasicek, A test for normality based on sample entropy. J. Royal Stat. Soc., Series B 38 (1976), pp. 54–59.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• H. Wu, and J. Lin, A scaled F-distribution as approximation to the distribution of test statistic in covariance structure analysis. Struct. Equation Model.: Multi. J. 23 (2016), pp. 409–421. doi: 10.1080/10705511.2015.1057733
   Web of Science ®Google Scholar
• F. Yousefzadeh, and N.R. Arghami, Testing exponentiality based on type II censored data and a new cdf estimator. Commun. Stat. Simul. Comput. 37 (2008), pp. 1479–1499. doi: 10.1080/03610910802178372
   Web of Science ®Google Scholar
• K.H. Yuan, W. Chan, G.A. Marcoulides, and P.M. Bentler, Assessing structural equation models by equivalence testing with adjusted fit indexes. Struct. Equation Model.: Multi. J. 23 (2016), pp. 319–330. doi: 10.1080/10705511.2015.1065414
   Web of Science ®Google Scholar