TESTING THE POPULATION INVERSE-COEFFICIENTS OF VARIATION AND ITS APPLICATION
Abstract
In this paper, some tests are introduced and compared for testing the equality of inverse-coefficients of variation. Monte-Carlo simulation method is used for comparisons. In this simulation study, various simulation scenarios were designed with different population numbers (k = 3, 6), sample sizes, parameter values and type I error rates (alpha = 0.01, 0.05). The tests were compared in terms of type I error rate and power in these scenarios. When the sample sizes are small, the D and WT tests showed good results in terms of type I error, but the LR and ST tests did not give good results. As the sample sizes increased, the experimental type I error rates of the LR and ST tests converged to the nominal type I error and all tests showed good results in general. While the sample sizes were equal, it was found that the LR test was the most powerful test and the ST test sometimes yielded good results. For these sample sizes, the D test yielded the worst results. When the sample sizes are different, the LR and D tests are powerful than the other tests, and the ST test is the worst test in terms of power. As expected, as the sample sizes and nominal type I error rate increased, the powers of the tests also increased. In addition, an application for the tests was made on real data. It was seen that the results of this application and simulation study coincide.
Keywords
Inverse-Coefficient of Variation,Monte-Carlo Simulation,Likelihood Ratio Test,Score Test,Wald Test
References
- [1] Bennett, B.M. On an Approximate Test for Homogeneity of Coefficients of Variation. Contributions to Applied Statistics 1976; 169-171.
- [2] Bowman, K.O., Shenton, L. R. Moment series for the coefficients of variation in Weibull sampling. American Statistical Associations 1981;148-153.
- [3] Chaturvedi, A., Rani, U. Fixed width confidence interval estimation of the inverse coefficient of variation in a normal population. Microelectronics and Reliability 1996; 36: 1305-1308.
- [4] Cox, D.R., Hinkley, D.V. Theoretical Statistics, Chapman and Hall. Londan, 111-119, 1974.
- [5] Doornbos, R., Dijkstra, J.B. A Multi-Sample Test for The Equality of Coefficients of Variation in Normal Population. Commun.Statist-Simula.Computa. 1983; 12: 147-158.
- [6] Gezgen Kesen, G., Potas, N., Visal Okur, F., Ok Bozkaya, I.,Aksu, T., Kuşkonmaz, B.B., Uçkan Çetinkaya, D.,Özbek, N. Y. Çocuklarda Hematopoetik Kök Hücre Naklisonrasi Prognozu Belirlemede Modifiye Ebmt Risk skorlamasinin Kullanımı. 10. Ulusal Kemik İliği Transplantasyonu ve Hücresel Tedaviler Kongresi; 1-3 Mart 2018; Antalya. Türkiye: pp. 99.
- [7] Kalkur, A.T., Rao, A. Bayes Estimator for Coefficient of Variation and Inverse Coefficient of Variation for the Normal Distribution. International Journal of Statistics and Systems 2017; 12:721-732.
- [8] Kendall, M., Stuart, A. The Advanced Theory of Statistics. Charles Griffin and Co., Londan, 205-210, 1977.
- [9] Lehmann, E.L., Casella, G. Theory of Point Estimation 2ed. Springer-Verlag, New York, 454-457,1998.
- [10] Nairy, K.S., Rao, K.A. Test of Coefficients of Variation of Normal Population. Commun.Statist-Simula.Computa. 2003; 32: 641-661.