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Original Articles

Two new estimators of entropy for testing normality

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Pages 5392-5411 | Received 14 May 2013, Accepted 01 Jul 2014, Published online: 11 Jul 2016

References

  • Alizadeh Noughabi, H., Arghami, N. (2011). Monte Carlo comparison of seven normality tests. J. Stat. Comput. Simul. 81:965–972.
  • Alizadeh Noughabi, H. (2010). A new estimator of entropy and its application in testing normality. J. Stat. Comput. Simul. 80:1151–1162.
  • Balakrishnan, N., Brito, M.R., Quiroz, A.J. (2013). On the goodness-of-fit procedure for normality based on the empirical characteristic function for ranked set sampling data. Metrika. 76:161–177.
  • Balakrishnan, N., Li, T. (2008). Ordered ranked set samples and applications to inference. J. Stat. Plann. Inference. 138:3512–3524.
  • Billingsley, P. (1995). Probability and Measure. New York: Wiley.
  • Brockwell, P., Davis, R.A. (1990). Time series: Theory and Method. New York: Springer Series in Statistics.
  • Chen, Z., Bia, Z., Sinha, B.K. (2004). Ranked set sampling. Theory and applications. Lecture notes in statistics, 176, New York: Springer.
  • Chhikara, R.S., Folks, J.L. (1977). The inverse Gaussian distribution as a lifetime model. Technometrics. 19:461–468.
  • Correa, J.C. (1995). A new estimator of entropy. Commun. Stat.: Theory Method. 24:2439–2449.
  • Dell, T.R., Clutter, J.L. (1972). Ranked set sampling theory with order statistics background. Biometrics 28:545–555.
  • Ebrahimi, N., Pflughoeft, K., Soofi, E.S. (1994). Two measures of sample entropy. Stat. Probab. Lett. 20:225–234.
  • Ebrahimi, N., Habibullah, M., Soofi, E. (1992). Testing exponentiality based on Kullback-Leibler information. J. Royal Stat. Soc.: Ser. B. 54:739–748.
  • Epps, T.W., Pulley, L.B. (1983). A test for normality based on the empirical characteristic function. Biometrika 70:723–726.
  • Esteban, M.D., Castellanos, M.E., Morales, D., Vajda, I. (2001). Monte Carlo comparison of four normality tests using different entropy estimates. Commun. Stat.: Simul. Comput. 30:761–785.
  • Grzegorzewski, P., Wieczorkowski, R. (1999). Entropy-based goodness-of-fit test for exponentiality. Commun. Stat.: Theory Methods 28:1183–1202.
  • Lee, S., Vonta, I., Karagrigoriou, A. (2011). A maximum entropy type test of fit. Comput. Stat. Data Anal. 55:2635–2643.
  • MacEachren, S.N., Ozturk, O., Wolfe, D.A., Stark, G.V. (2002). A new ranked set sample estimator of variance. J. Royal Stat. Soc.: Ser. B. 64:177–188.
  • McIntyre, G.A. (1952). A method for unbiased selective sampling using ranked set sampling. Aust. J. Agric. Res. 3:385–390.
  • Mudholkar, G.S., Natarajan, R., and Chaubey, Y.P. (2001). A goodness-of-fit test for the inverse Gaussian distribution using its independence characterization. Sankhya: Indian J. Stat. 63:362–374.
  • Ning, W., Ngunkeng, G. (2013). An empirical likelihood ratio based goodness-of-fit test for skew normality. Stat. Methods Appl. 22:209–226.
  • Park, S., Park, D. (2003). Correcting moments for goodness of fit tests based on two entropy estimates. J. Stat. Comput. Simul. 73:685–694.
  • Patil, G.P., Sinha, A.K., Taillie, C. (1999). Ranked set sampling: a bibliography. Environ. Ecol. Stat. 6:91–98.
  • Rezakhah, S., Shemesavar, S. (2009). New features on real zeros of random polynomials. Nonlin. Anal.: Theory Methods Appl. 71:2233–2238.
  • Shannon, C.E. (1948). A mathematical theory of communications. Bell Syst. Tech. J. 27:379–423;623–656.
  • Stokes, S.L. (1980). Estimation of variance using judgement ordered ranked set samples. Biometrics 36:35–42.
  • Stokes, S.L., Sager, T.W. (1988). Characterization of a ranked-set sample with application to estimating distribution function. J. Am. Stat. Assoc. 83:374–381.
  • Takahasi, K., Wakimoto, K. (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann. Inst. Stat. Math. 20:1–31.
  • Van Es, B. (1992). Estimating functionals related to a density by class of statistics based on spacings. Scand. J. Stat. 19:61–72.
  • Vasicek, O. (1976). A test for normality based on sample entropy. J. Royal Stat. Soc.: Ser. B. 38:54–59.
  • Von Alven, W.H. (1964). Reliability Engineering, ARINC Research Corporation. Englewood Cliffs, New Jersey: Prentice-Hall Inc.
  • Wieczorkowski, R., Grzegorzewsky, P. (1999). Entropy estimators improvements and comparisons. Commun. Stat.: Simul. Comput. 28:541–567.
  • Zamanzade, E., Arghami, N.R. (2012). Testing normality based on new entropy estimators. J. Stat. Comput. Simul. 82:1701–1713.

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