<?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>0120-1751</journal-id>
<journal-title><![CDATA[Revista Colombiana de Estadística]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.Colomb.Estad.]]></abbrev-journal-title>
<issn>0120-1751</issn>
<publisher>
<publisher-name><![CDATA[Departamento de Estadística - Universidad Nacional de Colombia.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-17512018000100087</article-id>
<article-id pub-id-type="doi">10.15446/rce.v41n1.57803</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A Bivariate Model based on Compound Negative Binomial Distribution]]></article-title>
<article-title xml:lang="es"><![CDATA[Un modelo basado en bivariadas compuesto distribución binomial negativa]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Omair]]></surname>
<given-names><![CDATA[Maha]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Almuhayfith]]></surname>
<given-names><![CDATA[Fatimah]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Alzaid]]></surname>
<given-names><![CDATA[Abdulhamid]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,King Saud University  ]]></institution>
<addr-line><![CDATA[Riyadh ]]></addr-line>
<country>Saudi Arabia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,King Faisal University  ]]></institution>
<addr-line><![CDATA[Alahsa ]]></addr-line>
<country>Saudi Arabia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>41</volume>
<numero>1</numero>
<fpage>87</fpage>
<lpage>108</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-17512018000100087&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-17512018000100087&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-17512018000100087&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract A new bivariate model is introduced by compounding negative binomial and geometric distributions. Distributional properties, including joint, marginal and conditional distributions are discussed. Expressions for the product moments, covariance and correlation coefficient are obtained. Some properties such as ordering, unimodality, monotonicity and self-decomposability are studied. Parameter estimators using the method of moments and maximum likelihood are derived. Applications to traffic accidents data are illustrated.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Un nuevo modelo de dos variables se introduce mediante la composición distribuciones binomiales negativos y geométricos. propiedades distributivas, incluyendo distribuciones conjuntas, marginales y condicionales se discuten. se obtienen las expresiones para los momentos de productos, la covarianza y el coeficiente de correlación. Se estudian algunas propiedades tales como pedidos, unimodalidad, monotonía y la auto-decomposability. Estimadores de parámetros utilizando el método de los momentos y de máxima verosimilitud se derivan. Aplicaciones a los datos de accidentes de tráfico se ilustran.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Bivariate distribution]]></kwd>
<kwd lng="en"><![CDATA[Compound distribution]]></kwd>
<kwd lng="en"><![CDATA[Correlation coefficient]]></kwd>
<kwd lng="en"><![CDATA[Divisibility]]></kwd>
<kwd lng="en"><![CDATA[Geometric distribution]]></kwd>
<kwd lng="en"><![CDATA[Moments]]></kwd>
<kwd lng="en"><![CDATA[Negative binomial distribution]]></kwd>
<kwd lng="en"><![CDATA[Total positivity]]></kwd>
<kwd lng="es"><![CDATA[coeficiente de correlación]]></kwd>
<kwd lng="es"><![CDATA[distribución binomial negativa]]></kwd>
<kwd lng="es"><![CDATA[distribución bivariada]]></kwd>
<kwd lng="es"><![CDATA[distribución compuesto]]></kwd>
<kwd lng="es"><![CDATA[distribución geométrica]]></kwd>
<kwd lng="es"><![CDATA[divisibilidad]]></kwd>
<kwd lng="es"><![CDATA[momentos]]></kwd>
<kwd lng="es"><![CDATA[positividad total]]></kwd>
</kwd-group>
</article-meta>
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