Resumen

NAVA, F. A.. Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies. Geofís. Intl [online]. 2023, vol.62, n.3, pp.519-523.  Epub 03-Jun-2024. ISSN 2954-436X.  https://doi.org/10.22201/igeof.2954436xe.2023.62.3.1578.

The Kullback-Leibler divergence, κ, is a widely used measure of the difference between an observed probability distribution and a reference one; κ=0 when the two distributions are equal, but it has no upper limit to help interpret the significance of any other κ value. Using as an example the problem of distinguishing clustering or gaps in the time occurrence of earthquakes from seismicity uniformly distributed in time, a Monte Carlo method for evaluating the significance of a particular κ value is presented, a method that takes into account the number of classes in the distributions and the length of the sample. Application of this method yields a probability according to which the hypothesis of the observed distribution being a realization of the reference one can be discarded or accepted with a quantitative degree of confidence. This method, and two possible reference values, are presented using the Poisson distribution as an example, but they can be used for other reference distributions.

Palabras llave : Kullback-Leibler divergence; Poisson distribution; Statistical seismology.