Published

2010-07-01

VERIFICACIÓN Y MONITOREO DE LA ALEATORIEDAD DE LOS JUEGOS DE NÚMEROS DE d DÍGITOS

TESTING AND MONITORING THE RANDOMNESS OF d DIGIT NUMBER GAME

Keywords:

carta de control, distribución geométrica, distribución multinomial, distribución Dirichlet, lotería, prueba ji-cuadrada (es)
Control chart, Dirichlet distribution, Geometric distribution, Lottery Chi-square test, Multinomial distribution (en)

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Authors

  • Humberto Gutiérrez-Pulido Universidad de Guadalajara
  • Juan Manuel García Universidad de Guadalajara
El interés de este trabajo se centra en el problema de probar la aleatoriedad de los resultados de los juegos de números de d dígitos. Es usual que este problema se aborde con pruebas aproximadas del tipo χ² y otras pruebas de independencia de resultados sucesivos. Pero estas pruebas, tienen entre otras limitantes, el hecho de que requieren muestras grandes. Como alternativa, en este trabajo se detalla una prueba bayesiana basada en el modelo multinomial. Además, para monitorear los resultados de este tipo de juego de azar y detectar en forma oportuna patrones y resultados no aleatorios, se propone la utilización de una carta de control geométrica. Se hace un breve estudio Monte Carlo para comprender mejor las características de la carta propuesta. Como caso práctico se analizan los resultados de 500 sorteos de la lotería mexicana Tris y se detectan problemas de falta de aleatoriedad, tanto con la prueba bayesiana como con la carta de control.
This work is centered on testing the randomness of d-digit number game. It is usual that this problem is studied by the χ² test and other tests for independence of successive draws. However, these tests require of large sample sizes. As an alternative, it is proposed a Bayesian methodology based on the multinomial model. This methodology does not depend on asymptotic results. Besides, for monitoring the results of this type of game, it is proposed a geometric control chart. Monte Carlo study is carried out to analyze this chart. As a practical case, the data of 500 draws of mexican lottery Tris were analyzed, and problems of lack of randomness are detected.

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How to Cite

Gutiérrez-Pulido, H., & García, J. M. (2010). TESTING AND MONITORING THE RANDOMNESS OF d DIGIT NUMBER GAME. Revista Colombiana De Estadística, 33(2), 167-190. https://revistas.unal.edu.co/index.php/estad/article/view/29815

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