<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0016-7169</journal-id>
<journal-title><![CDATA[Geofísica internacional]]></journal-title>
<abbrev-journal-title><![CDATA[Geofís. Intl]]></abbrev-journal-title>
<issn>0016-7169</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Geofísica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0016-71692023000300519</article-id>
<article-id pub-id-type="doi">10.22201/igeof.2954436xe.2023.62.3.1578</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Significance estimation for the Kullback-Leibler divergence: the Poissonian case in seismological studies]]></article-title>
<article-title xml:lang="es"><![CDATA[Estimación de significatividad para la divergencia Kullback-Leibler: el caso Poissoniano en estudios sismológicos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Nava]]></surname>
<given-names><![CDATA[F. A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Centro de Investigación y de Educación Superior de Ensenada Departamento de Sismología ]]></institution>
<addr-line><![CDATA[ B.C.]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>09</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>09</month>
<year>2023</year>
</pub-date>
<volume>62</volume>
<numero>3</numero>
<fpage>519</fpage>
<lpage>523</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0016-71692023000300519&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0016-71692023000300519&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0016-71692023000300519&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The Kullback-Leibler divergence, &#954;, is a widely used measure of the difference between an observed probability distribution and a reference one; &#954;=0 when the two distributions are equal, but it has no upper limit to help interpret the significance of any other &#954; 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 &#954; 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.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen La divergencia Kullback-Leibler, &#954;, es una medida ampliamente usada de la diferencia entre una distribución de probabilidad observada y otra distribución de referencia; &#954;=0 cuando ambas distribuciones son iguales, pero no tiene un valor tope que permita interpretar la significatividad de cualquier otro valor de &#954;. Usando como ejemplo el problema de distinguir cúmulos o vacancias en la ocurrencia temporal de sismos de sismicidad distribuida con probabilidad uniforme en el tiempo, se presenta un método de Monte Carlo para evaluar la significatividad de algún valor de &#954;, método que toma en cuenta el largo de la muestra. Este método y dos posibles valores de referencia son presentados usando la distribución de Poisson como ejemplo, pero pueden ser utilizados con cualquier otra distribución de referencia.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Kullback-Leibler divergence]]></kwd>
<kwd lng="en"><![CDATA[Poisson distribution]]></kwd>
<kwd lng="en"><![CDATA[Statistical seismology]]></kwd>
<kwd lng="es"><![CDATA[Divergencia Kullback-Leibler]]></kwd>
<kwd lng="es"><![CDATA[Distribución de Poisson]]></kwd>
<kwd lng="es"><![CDATA[Sismología estadística]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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