New Modified Anderson Darling Goodness of Fit Test for Lognormal and Gamma distributions
Keywords:Goodness of fit test, Anderson-Darling test, Kolmogorov Smirnov test, Modified Anderson-Darling test
The purpose of this study is to present the new modified Anderson-Darling goodness of fit test, and compare to the efficiency of three tests; Kolmogorov Smirnov test, Anderson-Darling test and Zhang (2002) test. A simulation study is used to estimate the critical values at a significance level of 0.05. The type I error rate and test power are calculated using Monte Carlo simulation with 10,000 replicates. The data are generated from the specified distribution; i.e., Lognormal and Gamma distributions with sample size of 10, 20, 30, 50, 100 and 200. The results demonstrate that every test has control over the type I error probability. The new test has the highest power for two alternative hypotheses; Loglogistic and Logistic distributions. Moreover, when the alternative distribution is Normal distribution and the sample size is small, the new test has the highest power.
Zhang, J. (2002). Powerful Goodness-of-Fit Tests Based on the Likelihood Ratio. Journal of the Royal Statistical Society Series B, 64(2), 281-294. DOI: 10.1111/1467-9868.00337
Cressie, N. & Read, T.M.C. (1984). Multinomial Goodness-of-Fit Tests. Journal of the Royal Statistical Society Series B, 46(3), 440-464. Available at: https://www.jstor.org/stable/2345686
Anderson, T.W. & Darling, D.A. (1952). Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes. The Annals of Mathematical Statistics, 23(2), 193-212.
Anderson, T.W. & Darling, D.A. (1954). A Test of Goodness of Fit. Journal of the American Statistical Association, 49(268), 765-769.
Yodsima, R., Pongsakchat, V., Phuenaree, B. & Neamvonk, J. (2016). A study on the distributions of goodness of fit test statistics. Proceedings The 8th Science Research Conference. 135-141.
Morgan, E.C., Lackner, M., Vogel, R.M., & Baise, L.G. (2011). Probability distributions for offshore wind speeds. Energy Conversion and Management, 52(1), 15-26. doi:10.1016/j.enconman.2010.06.015
Dikko, H.G., David, I.J., & Bakari, H.R. (2013). Modeling the Distribution of Rainfall Intensity using Quarterly Data. IOSR Journal of Mathematics, 9(1), 11-16. DOI:10.9790/5728-0911116
Ximenes, P.S.M.P., Silva, A.S.A., Ashkar, F., & Stosic, T.(2021). Best-fit probability distribution models for monthly rainfall of Northeastern Brazil, 84(6), 1541-1556. DOI: 10.2166/wst.2021.304
Arthur, Y.D., Gyamfi, K.B. & Appiah, S.K. (2013). Probability Distributional Analysis of Hourly Solar Irradiation in Kumasi-Ghana. International Journal of Business and Social Research3(3), 63-75. DOI:10.18533/ijbsr.v3i3.57
Magenuka, T.K.M., Musasa, K. & Akindeji, K.T. (2020). Kernel Density Estimation of Solar Radiation and Wind Speed for South Africa. Proceedings of the 5th NA International
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