Testing Homogeneity for Poisson Processes

• RAÚL FIERRO ^[1] ; ALEJANDRA TAPIA ^[2]
  1. [1] Pontificia Universidad Católica de Valparaíso

     Pontificia Universidad Católica de Valparaíso

     Valparaíso, Chile

     
  2. [2] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 34, Nº. 3, 2011, págs. 421-432
• Idioma: inglés
• Títulos paralelos:
  • Prueba de homogeneidad para procesos de Poisson
• Enlaces
  • Texto completo
• Resumen
  • español

    Una prueba de hipótesis asintótica para verificar homogeneidad de un proceso de Poisson sobre ciertos subintervalos es desarrollada. Bajo la hipótesis nula, estimadores máximo verosímiles para los valores de la función intensidad sobre los subintervalos mencionados son determinados y usados en el test de homogeneidad.

  • English

    We developed an asymptotically optimal hypothesis test concerning the homogeneity of a Poisson process over various subintervals. Under the null hypothesis, maximum likelihood estimators for the values of the intensity function on the subintervals are determined, and are used in the test for homogeneity.

• Referencias bibliográficas
  • Arkin, B. L.,Leemis, L. M.. (2000). 'Nonparametric estimation of the cumulative intensity function for a nonhomogeneous Poisson process...
  • Fierro, R.. (2008). 'Test of homogeneity for some population models based on counting processes'. Communications in Statistics-Theory...
  • Henderson, S. G.. (2003). 'Estimation for nonhomogeneous Poisson processes from aggregated data'. Operation Research Letters. 31....
  • Karr, A. F.. (1991). Point Processes and their Statistical Inference. Marcel Dekker.
  • Kuhl, M. E.,Wilson, J. R.. (2000). 'Least square estimation of nonhomogeneous Poisson processes'. Journal of Statistical Computation...
  • Kuhl, M. E.,Wilson, J. R.,Johnson, M. A.. (1997). 'Estimating and simulating Poisson processes having trends or multiple periodicities'....
  • Leemis, L. M.. (1991). 'Nonparametric estimation of the cumulative intensity function for a nonhomogeneous Poisson process'. Management...
  • Leemis, L. M.. (2004). 'Nonparametric estimation and variate generation for a nonhomogeneous Poisson process from event count data'....
  • Lehmann, E. L.. (1999). Elements of Large-Sample Theory. Springer-Verlag.
  • Lewis, P. A. W.,Shedler, G. S.. (1979). 'Simulation of nonhomogeneous Poisson process by thinning'. Naval Research Logistics. 26....
  • Neyman, J.. (1949). Contribution to the theory of the \chi^2 test. 'First Berkeley Symposium on Mathematical Statistics and Probability'....
  • Roberts, S. W.. (1966). 'A comparison of some control chart procedures'. Technometrics. 8. 411-430
  • Serfling, R. J.. (1980). Approximation Theorems of Mathematical Statistics. Wiley and Sons.
  • Shiryaev, A. N.. (1963). 'On optimum methods in quickest detection problems'. Theory Probability and Its Applications. 8. 22-46