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.

Key words: Poisson process, hypothesis testing, local alternatives, asymptotic distribution, asymptotically optimal, likelihood ratio test.

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.

Palabras clave: proceso de Poisson, prueba de hipótesis, alternativas locales, distribución asintótica, asintóticamente óptimo, prueba de razón de verosimilitud.

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