Revista Colombiana de Estadística
Print version ISSN 0120-1751
Combining the runs theory developed by Corzo (1989) and the idea of Modarres & Gastwirth (1996), which uses the number of runs left after cutting the dichotomized succession, three families of statistics based on runs and three tests for the hypothesis of symmetry are proposed. Using the linearization Taylor's technique, the expected value and variance of two from the three proposed families is approximated. A study to aproximate the distribution of the statistics through the normal distribution for the studied sample sizes is realized. The proposed tests are compared in terms of their power with some other recent and common nonparametric tests for Symmetry, for the sample sizes n=10(1)25, n=30, n=50(50)250 and n=500. For this comparison, Monte Carlo methods were used and the samples were generated from nine distributions obtained from the generalized lambda distribution. The simulations indicate that, for a wide variety of asymmetric alternatives in the generalized lambda distribution, the tests proposed are more powerful than the existing tests in literature.
Keywords : Lambda distribution; Power; Runs test; Symmetry test.