ADK divergence measure and testing exponentiality based on estimated ADK information

 
 
 
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  • References
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  • Abstract


    In this paper, I define the two parameter ADK divergence measure, as a generalized of Re'nyi divergence measure. Also I introduce a goodness of t tests for exponentiality based on the estimated ADK information. I use an estimator for ADK distance in manner of Correa estimate. Critical values of the test are obtained by Monte Carlo simulation. The power of the test is computed under gamma distribution.

    Keywords: KADK entropy; Renyi entropy; Shannon entropy; Kullback - Leibler divergence measure; Renyi divergence measure; ADK divergence measure; Exponentiality test; Critical value.


  • References


      Abbasnejad, M. and Shakuri, M. (2008), A goodness of fit test for exponentiality based ok estimated Renyi information, Journal of Statistical Sciences, Vol. 2, No. 2, 201-211.
    1. Alizadeh Noughabi H. , Arghami, N. R. and Alizadeh Noughabi R. (2008), Comparison of different entropy estimators and power of exponentiality tests based on entropy estimators, Journal of Statistical Sciences, Vol. 2, No. 2, 213-227.
    2. Alizadeh Noughabi H. , Arghami, N. R. (2011), Monte Carlo comparison of five exponentiality tests using different entropy estimates. Journal of Statistical Computation and Simulation Vol. 81, No. 11, November 2011, 15791592.
    3. A. Renyi, 1961, On measures of entropy and information, in: Proceedings of the Fourth Berkeley Symposium on Mathematics, Statistics and Probability, vol. 1, University California Press, Berkeley, 547-561.
    4. A. Renyi, 1965, On the foundation of information theory, Rev. Inst. Int. Stat. 33 1-14.
    5. Baringhaus, L. and Henze, N. (2000). Tests of fit for exponentiality based on a characterization via the mean residual life function, Statistical Papers 41, 225-236.
    6. C. Arndt, 2001, Information Measures, Springer, Berlin.
    7. C.E. Shannon, 1984, A mathematical theory of communication, Bell Syst. Tech. J 27 379-423. 623-656.
    8. Ebrahimi, N., Soofi, E.S. and Habibullah, M. (1992). Testing Exponentiality Based on Kullback-Leibler Information, Journal of the Royal Statistical Society B 54, 739-748.
    9. Finkelsein, J. and Schafer, R.E. (1971), Imported goodness of fit tests, Biometrika, 58, 641-645.
    10. Henze, N. (1993). A New Flexible Class of Omnibus Tests for Exponentiality, Communications in Statistics Theory and Methods 22, 115-133.
    11. J. Aczel and Z. Daroczy, 1963, Characterisierung der entropien positiver ordnung und der Shannons chen entropie. Act.Math.Acad.Sci.Hunger 14, 95-121.
    12. J.N. Kapur, 1967, Generalized entropy of order and type . The Math. Seminar 4 78-82.
    13. Khodabin, M. , (2011), Some properties of ADK entropy and ADK entropy rate, Procedia Computer Science 3, 11701177.
    14. Khodabin, M. , (2010), ADK entropy and ADK entropy rate in irreducible aperiodic Markov chain and Gaussian processes, JIRSS, accepted manuscript, and it will appear in Vol.9, No. 2.
    15. Kullback, S. (1959), Information Theory and Statistics. New York: John Wiley.
    16. Lillifors, H. W. (1969), On the Kolmogorov test for the exponential distribution with mean unknown, Journal of American Statistical Association,64,387-389.
    17. Park, S. (2005), Testing exponentiality based on the Kullback- Leibler information with the type II censored data. IEEE Trans. on Rel., 54, 22-26.
    18. Pham, H. (Ed.), 2003. Handbook of Reliability Engineering. Springer, London.
    19. Van-Soset, J. (1969), Some goodness of fit tests for exponential distribution, Statistica Neerlandica, 23, 41-51.
    20. Vasicek, O. (1976), A test for normality based on sample entropy, Journal of the Royal Statistical Society, 38, 54-59.
    21. Yousefzadeh, F. and Arghami, N.R. (2008), Testing exponentiality based on type II censored data and new cdf estimator, Communications in Statistics, Simulation and Computation, 37, 1479-1499.
    22. Zamanzadeh, E. and Arghami, N. R. (2008), Normality and exponentiality tests based on new entropy estimators, Journal of Statistical Sciences, Vol. 2, No. 2, 179-200.

 

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Article ID: 3485
 
DOI: 10.14419/ijamr.v3i4.3485




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