Published

2010-07-01

PROPUESTA DE UNA PRUEBA DE RACHAS RECORTADA PARA HIPÓTESIS DE SIMETRÍA

A PROPOSED RUNS TRIMMING TEST FOR THE HYPOTHESIS OF SYMMETRY

Keywords:

distribución lambda generalizada, potencia, pruebas de rachas, pruebas para simetría (es)
Lambda distribution, Power, Runs test, Symmetry test (en)

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Authors

  • Giovany Babativa Universidad Nacional de Colombia
  • Jimmy A. Corzo Universidad Nacional de Colombia
Combinando la teoría de rachas desarrollada por Corzo (1989) y la idea de Modarres & Gastwirth (1996), que utilizan el número de rachas que quedan después de recortar la sucesión dicotomizada, se proponen tres pruebas de rachas para la hipótesis de simetría. Utilizando la técnica de linealización de Taylor se aproxima el valor esperado y la varianza, y se realiza un estudio de aproximación de la distribución del estadístico por la distribución normal. Las pruebas propuestas son comparadas en términos de su potencia con algunas de las pruebas no paramétricas más recientes y comunes para dicho problema en tamaños de muestra n = 10(1)25, n = 30, n = 50(50)250 y n = 500. Para la comparación se utilizaron métodos de Monte Carlo, y las muestras fueron generadas de nueve distribuciones pertenecientes a la familia lambda generalizada (DLG). Las simulaciones indican que para una gran variedad de alternativas asimétricas las pruebas propuestas son más potentes que las pruebas existentes en la literatura.
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 Taylorts 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.

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Babativa, G., & Corzo, J. A. (2010). A PROPOSED RUNS TRIMMING TEST FOR THE HYPOTHESIS OF SYMMETRY. Revista Colombiana De Estadística, 33(2), 251-271. https://revistas.unal.edu.co/index.php/estad/article/view/29821

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