A Runs Test for the Hypothesis of Symmetry with one Sided Alternative
http://orcid.org/0000-0002-3730-7685
Myrian Elena Vergara_Morales
http://orcid.org/0000-0003-1198-0051
José Giovany Babativa-Márquez
##plugins.themes.bootstrap3.article.details##
We propose a trimmed runs test for the hypothesis of symmetry with one sided alternative, in samples coming from the Generalized Lambda Distribution (GLD) with unknown median. We provide a method to calculate the exact distribution, showing that it is symmetric around zero and we give arguments to justify the approximation by means of the normal distribution. The size of the proposed test is calibrated with four symmetrical cases of the GLD and the empirical power is compared with that of some other tests for the same hypothesis, using eight asymmetrical cases of the GLD. The results show that the proposed test is unbiased in the cases used for calibration, and that the empirical power of the proposed test overtakes the empirical power of all compared tests, excepting one of them in two specific cases. Some hints are given concerning how to optimize the empirical power according to the size of the tails of the sampled distributions.
Runs tests, Power of a test, One Sided Symmetry Tests
http://www.shanghairanking.com/ARWU2018.html
Babativa G, Corzo JA. Propuesta de una prueba de rachas recortada para hipótesis de simetría, Revista Colombiana de Estadística, 33(251): 271, 2010.
doi: 10.15446/rce
Baklizi A. Testing symmetry using a trimmed longest run statistic, Australian New Zealand Journal of Statistics, 49(4): 339-347, 2007.
doi: 10.1111/j.1467-842X.2007.00485.x
Cabilio P, Masaro J. A simple test of symmetry about an unknown median, The Canadian Journal of Statistics, 24(3): 349-361, 1996.
doi: 10.2307/3315744
Chatterjee S, Sen P. On Kolmogorov-Smirnov-Type Tests for Symmetry, Annals of the Institute of Statistical Mathematics, 25(1): 287-299, 1971.
doi: 10.1007/BF02479375
Cheng W, Balakrishnan N. A modified sign test for symmetry, Communications in Statistics Simulation and Computation, 33: 703-709, 2004.
doi: 10.1081/SAC-200033302
Corzo J, Babativa G. A modified runs test for symmetry, Journal of the Statistical Computation and Simulation, 83(5): 984-991, 2013.
doi: 10.1080/00949655.2011.647026
Hall P, Heyde CC. Martingale limit theory and its application, Academic press, New York, 1980.
ICFES. Instituto colombiano para el fomento de la educación superior, Saber Pro, 2018.
ftp://ftp.icfes.gov.co/
McWilliams P. A Distribution-Free Test for Symmetry Based on a Runs Statistic, Journal of the American Statistical Association, 85(412): 1130-1133,1990.
doi: 10.1080/01621459.1990.10474985
Miao W, Gel Y, Gastwirth J. A new test of symmetry about an unknown median, Random Walk, Sequential Analysis and Related Topics - A Festschrift in Honor of Yuan-Shih Chow. Eds.: Agnes Hsiung, Cun- Hui Zhang, and Zhiliang Ying, World Scientific Publishing, pp. 1-19, 2006.
doi: 10.1142/9789812772558_0013
Mira A. Distribution-free test for symmetry based on Bonferroni’s measure, Journal of Applied Statistics, 26(8): 959-972, 1999.
doi: 10.1080/02664769921963
Modarres R, Gastwirth JL. A modified runs test for symmetry, Statistics & probability letters, 31(2): 107-112, 1996.
doi: 10.1016/S0167-7152(96)00020-X
Noughabi HA. Tests of symmetry based on the sample entropy of order statistics and power comparison, Sankhya B, 77(2): 240-255, 2015.
Welch BL. The significance of the difference between two means when the population variances are unequal, Biometrika, 29: 350-362, 1938.
doi: 10.1093/biomet/29.3-4.350