Üstel Dağılıma Uygunluk İçin Bazı Uyum İyiliği Testlerinin I.Tip Hata ve Güçleri Bakımından Kıyaslanmaları

İstatistiksel bir modelin uyum iyiliği gözlenen bir veri setinin istatistiksel modele uyumluluğunu test eder. Bu çalışmada Kolmogorov-Smirnov(1939), Lilliefors(1969), Anderson-Darling(1954), Entropiye dayalı uyum iyiliği testleri ( Ebrahimi(1991) , Choi (2004), Correa (1995), Noughabi(2010) ) ve Fortiana(2002) 'nın geliştirdikleri uyum iyiliği testleri üstel dağılım için incelenmiştir. Ayrıca bu test istatistikleri deneysel I.tip hata olasılığı ve testin gücü bakımından farklı dağılım şekilleri altında karşılaştırılmıştır.

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  • Choi, K.K. (2004). Goodness of fit tes for exponentiality based on Kullback-Leibler information. Commun. Stat. Simul. Comput. 33 , 525-536.
  • Cochran, W.G. (1952). The chi-square test of goodness of fit. The Annals of Mathematical Statistics , 315345.
  • Correa, J. (1995). A new estimator of entropy. Commun. Stat. Theory Methods 24 , 2439-2449.
  • Cramer, H. (1928). on the composition of elementary errors. Skand. Aktuar. 11 , 141-180.
  • Darling, T.W. (1954). A Test of Goodness of Fit. Journal of the American Statistical Association , 765769.
  • Es, B.V. (1992). Estimating functionals related to a density by class of statistics based on spacings. Scand. J. Stat , 61-72.
  • Noughabi, H. A, Arghami N.R. (2011). Monte Carlo comprassion of five exponentiality test using different entropy estimates. Journal of Statstical Computataion and Simulation , 1-14.
  • Fortiana, A.G. (2002). A scale-free goodness-of-fit statistic for the exponential distrubution based on maximum correlations. journal of statistical planning and inference , 85-97.
  • Kolmogorov, A.N. (1933). Sulla determinazone empirica di une legge di distribuzione. G. İst. Attuari , 8391.
  • Lilliefors, H. W. (1969). On the Kolmogorov-Smirnov Test for the Exponential Distribution with Mean. Journal of the American Statistical Association , 387-389.
  • Gail, J. L. (1978). A scale-free goodness of fit test for the exponential distribution based on the Gini statistic. Journal of the Royal Statistical Society , 350-357.
  • N.Ebrahimi, M.H. (1992). Testing Exponentiality based on Kullback-Leiber information. J.R. Statist. Soc. Ser. B54 , 739-748.
  • Noughabi, H.A (1992). A new estimator of entropy and its application in testing normality. J.Statis. Soc. Ser. B 54 , 1151-1162.
  • Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine series 5 , 157-175.
  • Shannon, C. (1948). A mathematical thory of communications. Bell Syst. Tech. J. 27 , 379-423.
  • Smirnov, N. (1939). On the estimation of the discrepancy between emprical curves of distribution for two independent samples. Bulletin of Moscow University , 3-16.
  • Stephens, M.A. (1976). Asymptotic results for goodness of fit statistics with unknown parameters. The Annals of Statistics , 357-369.
  • Wilk, S. (1972). An analysis of variance test for the exponential distrubutions complete samples. Technometrics , 355-370.
  • Noughabi, H.A and Arghami, N. R. General treatment of goodness-of-fit tests based on Kullback–Leibler information. Journal of Statistical Computation and Simulation, DOI: 10.1080/00949655.2012. 667100
  • Baratpour, S. and Rad, A.H. (2012) Testing Goodness-ofFit for Exponential Distribution Based on Cumulative Residual Entropy, Communications in Statistics - Theory and Methods, 41(8): 13871396