Comparisons of the Goodness of Fit Tests for the Geometric Distribution

Yıl 2013, Cilt: 26 Sayı: 3, 369 - 375, 22.02.2013

Deniz Özonur , Esra Gökpınar , Fikri Gökpınar , Hülya Bayrak , Hasan Gül

Öz

This article gives some goodness of fit tests for the Geometric distribution. The tests used in this study are Anderson Darling test, Cramer-von Mises test, Kolmogorov Smirnov test, test based on partition of Chi-square and some new alternatives based on smooth tests. The performance of these tests is compared by simulation study according to type-I errors and powers of tests. The power comparisons indicate that the modified version of smooth test statistic has the highest power value of test for Negative Binomial, Binomial and Poisson distributions. Also, Kolmogorov Smirnov, Anderson Darling, Cramer-von Mises and  test statistics can be preferred for large sample sizes.

 

 

Keywords: Anderson Darling test, Cramer-von Mises test, Kolmogorov Smirnov test, Chi-square test.

Anahtar Kelimeler

Anderson Darling test, Cramer-von Mises test, Kolmogorov Smirnov test, Chi-square test.

Kaynakça

• Internet: Jaggi, S. and Batra, P.K., In Indian Agricultural Statistics Research Institute Library Avenue http://www.iasri.res.in/ebook/EB_SMAR/index.htm , (2003). Online.
• Lee, J., "The Demand for varied diet with econometric models for count data", American Journal of Agricultural Economics, 69(3): 687- 692, (1987).
• Yen, S.T. and Adamowicz, W.L., "Statistical properties of welfare measures from count-data models of recreation demand", Rev. Agr. Econ., 15: 205-215, (1993).
• Hubbell, B.J., "Estimating insecticide application frequencies: A comparison of Geometric and count data models", Journal of Agricultural and Applied Economics, (29)2: 225-242, (1997).
• Choulakian, V., Lockhart, R.A. and Stephens, M.A., "Cramer-Von Mises tests for discrete distributions", Canadian Journal of Statistics, 22: 125-137, (1994).
• Lancaster, H.O., "A reconciliation of χ from 2 metrical and enumerative aspects", Sankhya, 13:1-10, (1953).
• Best, D.J. and Rayner, J.C.W., "Tests of fit for the Geometric distribution", Communications in Statistics-Simulation and Computation, 32(4): 1065-1078, (2003).
• Henze, N., "Empirical distribution function goodness of fit tests for discrete models", Canadian Journal of Statistics, 24: 81-93, (1996).
• Best, D.J. and Rayner, J.C.W., "Goodness of fit for the Geometric distribution", Biom. J., 31: 307-311, (1989).
• Rayner, J.C.W. and Best, D.J., Smooth tests of goodness of fit, Oxford University Press, New York, (1989).
• Spinelli, J.J. and Stephens, M.A., "Cramer-von Mises tests of fit for the Poisson distribution", Canadian Journal of Statistics, 25: 257-268, (1997).
• Bracquemond, C., Cretois, E. and Gaudoin, O., "A comparative study of goodness-of- fit tests for the Geometric distribution and application to discrete time reliability", Laboratoire Jean Kuntzmann, Computer Science, Technical Report, (2002). Mathematics and [13] Emerson, P.L., polynomials a orthogonal recurrence formula", Biometrics 24: 695-701, (1968). from general
• Rayner, J.C.W., Thas, O. and Best, D.J., Smooth tests of goodness of fit: Using R 2. ed., John Wiley and Sons, USA, (2009).