<?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>S0120-17512010000200003</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una extensión de la distribución Weibull de dos parámetros]]></article-title>
<article-title xml:lang="en"><![CDATA[An Extension of the Two-Parameter Weibull Distribution]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[OLIVARES-PACHECO]]></surname>
<given-names><![CDATA[JUAN F.]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[CORNIDE-REYES]]></surname>
<given-names><![CDATA[HÉCTOR C.]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[MONASTERIO]]></surname>
<given-names><![CDATA[MANUEL]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad de Atacama Facultad de Ingeniería Departamento de Matemática]]></institution>
<addr-line><![CDATA[Copiapó ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad de Atacama Facultad de Ingeniería Departamento de Ingeniería Informática y Ciencias de la Computación]]></institution>
<addr-line><![CDATA[Copiapó ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="A03">
<institution><![CDATA[,Universidad de Atacama Facultad de Ingeniería Departamento de Ingeniería Informática y Ciencias de la Computación]]></institution>
<addr-line><![CDATA[Copiapó ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>15</day>
<month>12</month>
<year>2010</year>
</pub-date>
<pub-date pub-type="epub">
<day>15</day>
<month>12</month>
<year>2010</year>
</pub-date>
<volume>33</volume>
<numero>2</numero>
<fpage>219</fpage>
<lpage>231</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-17512010000200003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-17512010000200003&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-17512010000200003&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[En este artículo se presenta una extensión de la distribución Weibull de dos parámetros, con el objetivo de flexibilizar el modelo en términos de la kurtosis. Se estudian las propiedades básicas de la nueva densidad obtenida, así como su función de distribución, momentos, coeficientes de asimetría y kurtosis. Se realizan estudios de simulación para algunos casos particulares, ilustrando la utilidad de la extensión considerada.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[In this paper, we present an extension of the Two-parameter Weibull distribution to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied. Simulation studies for some cases, illustrating the usefulness of the extension considered, are carried out.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[coeficiente de asimetría]]></kwd>
<kwd lng="es"><![CDATA[distribución Weibull]]></kwd>
<kwd lng="es"><![CDATA[kurtosis]]></kwd>
<kwd lng="es"><![CDATA[Slash]]></kwd>
<kwd lng="en"><![CDATA[Asymmetry]]></kwd>
<kwd lng="en"><![CDATA[Kurtosis]]></kwd>
<kwd lng="en"><![CDATA[Slash distribution]]></kwd>
<kwd lng="en"><![CDATA[Weibull distribution]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font size="2" face="verdana">      <p> <b> <font size="4">     <center> Una extensi&oacute;n de la distribuci&oacute;n Weibull de dos par&aacute;metros </center> </font> </b> </p>      <p> <b> <font size="3">     <center> An Extension of the Two-Parameter Weibull Distribution </center> </font> </b> </p>      <p>     <center> JUAN F. OLIVARES-PACHECO<sup>1</sup>,  H&Eacute;CTOR C. CORNIDE-REYES<sup>2</sup>,  MANUEL MONASTERIO<sup>3</sup> </center> </p>      <p> <sup>1</sup>Universidad de Atacama, Facultad de Ingenier&iacute;a, Departamento de Matem&aacute;tica, Copiap&oacute;, Chile. Instructor. Email: <a href="mailto:jolivares@mat.uda.cl">jolivares@mat.uda.cl</a>     <br>  <sup>2</sup>Universidad de Atacama, Facultad de Ingenier&iacute;a, Departamento de Ingenier&iacute;a Inform&aacute;tica y Ciencias de la Computaci&oacute;n, Copiap&oacute;, Chile. Profesor asistente. Email: <a href="mailto:hcornide@diicc.uda.cl">hcornide@diicc.uda.cl</a>     <br>  <sup>3</sup>Universidad de Atacama, Facultad de Ingenier&iacute;a, Departamento de Ingenier&iacute;a Inform&aacute;tica y Ciencias de la Computaci&oacute;n, Copiap&oacute;, Chile. Profesor asistente. Email: <a href="mailto:mmonasterio@diicc.uda.cl">mmonasterio@diicc.uda.cl</a>     ]]></body>
<body><![CDATA[<br> </p>  <hr size="1">      <p> <b>     <center> Resumen </center> </b> </p>      <p> En este art&iacute;culo se presenta una extensi&oacute;n de la distribuci&oacute;n Weibull de dos par&aacute;metros, con el objetivo de flexibilizar el modelo en t&eacute;rminos de la kurtosis. Se estudian las propiedades b&aacute;sicas de la nueva densidad obtenida, as&iacute; como su funci&oacute;n de distribuci&oacute;n, momentos, coeficientes de asimetr&iacute;a y kurtosis. Se realizan estudios de simulaci&oacute;n para algunos casos particulares, ilustrando la utilidad de la extensi&oacute;n considerada. </p>      <p> <b> Palabras clave: </b> coeficiente de asimetr&iacute;a, distribuci&oacute;n Weibull, kurtosis, Slash. </p>  <hr size="1">      <p> <b>     <center> Abstract </center> </b> </p>      <p> In this paper, we present an extension of the Two-parameter Weibull distribution to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied. Simulation studies for some cases, illustrating the usefulness of the extension considered, are carried out. </p>      <p> <b> Key words: </b> Asymmetry, Kurtosis, Slash distribution, Weibull distribution. </p>  <hr size="1">      <p> Texto completo disponible en <a href="pdf/rce/v33n2/v33n2a03.pdf">PDF</a> </p>  <hr size="1">      ]]></body>
<body><![CDATA[<p> <b> <font size="3"> Referencias </font> </b> </p>       <!-- ref --><p> 1. Byrd, R. H., Lu, P., Nocedal, J. &amp; Zhu, C. (1995), 'A Limited Memory Algorithm for Bound Constrained Optimization', <i>SIAM Journal on Scientific Computing</i> <b>16</b>(5), 1190-1208. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000024&pid=S0120-1751201000020000300001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 2. Chen, Z. (2000), 'An New Two-parameter Lifetime Distribution with Bathtub-Shape or Increasing Failure Rate Function', <i>Statistics and Probability Letters</i> <b>49</b>(2), 155-161. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000025&pid=S0120-1751201000020000300002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 3. G&oacute;mez, H. W., Olivares-Pacheco, J. F. &amp; Bolfarine, H. (2009), 'An Extension of the Generalized Birnbaum-Saunders Distributions', <i>Statistics and Probability Letters</i> <b>79</b>(3), 331-338. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000026&pid=S0120-1751201000020000300003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 4. G&oacute;mez, H. W., Quintana, F. A. &amp; Torres, F. J. (2007), 'A New Family Slash-Distributions with Elliptical Contours', <i>Statistics and Probability Letters</i> <b>77</b>(7), 717-725. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000027&pid=S0120-1751201000020000300004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 5. Johnson, N. L., Kotz, S. &amp; Balakrishnan, N. (1995), <i>Continuous Univariate Distributions</i>, Second edn, Wiley, New York. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000028&pid=S0120-1751201000020000300005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 6. Kafadar, K. (1982), 'A Biweight Approach to the One-Sample Problem', <i>Journal of the American Statistical Association</i> <b>77</b>(378), 416-424. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000029&pid=S0120-1751201000020000300006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 7. Mosteller, F. &amp; Tukey, J. W. (1977), <i>Data Analysis and Regression</i>, Addison-Wesley. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000030&pid=S0120-1751201000020000300007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 8. Rogers, W. H. &amp; Tukey, J. W. (1972), 'Understanding Some Long-tailed Symmetrical Distribution', <i>Statistics Neerlandia</i> <b>26</b>, 211-226. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000031&pid=S0120-1751201000020000300008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 9. Tang, Y., Xie, M. &amp; Goh, N. T. (2003), 'Statistical Analysis of a Weibull Extension Model', <i>Communications in Statistics: Theory and Methods</i> <b>32</b>(5), 913-928. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000032&pid=S0120-1751201000020000300009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 10. Wang, J. &amp; Genton, M. G. (2006), 'The Multivariate Skew-Slash Distribution', <i>Journal of Statistical Planning and Inference</i> <b>136</b>(1), 209-220. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000033&pid=S0120-1751201000020000300010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p> 11. Zhang, T. &amp; Xie, M. (2007), 'Failure Data Analysis with Extended Weibull Distribution', <i>Communications in Statistics: Simulation and Computation</i> <b>36</b>(3), 579-592. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000034&pid=S0120-1751201000020000300011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><center> <b>&#91;Recibido en marzo de 2009. Aceptado en octubre de 2010&#93;</b> </center> <hr size="1">      <p> Este art&iacute;culo se puede citar en <i>LaTeX</i> utilizando la siguiente referencia bibliogr&aacute;fica de <i>BibTeX</i>: </p> <code><font size="2">@ARTICLE{RCEv33n2a03,    <br>  &nbsp;&nbsp;&nbsp; AUTHOR &nbsp;= {Olivares-Pacheco, Juan F. and Cornide-Reyes, H&eacute;ctor C. and Monasterio, Manuel},    <br>  &nbsp;&nbsp;&nbsp; TITLE &nbsp; = {{Una extensi&oacute;n de la distribuci&oacute;n Weibull de dos par&aacute;metros}},    <br>  &nbsp;&nbsp;&nbsp; JOURNAL = {Revista Colombiana de Estad&iacute;stica},    <br> &nbsp;&nbsp;&nbsp; YEAR &nbsp;&nbsp; = {2010},    <br> &nbsp;&nbsp;&nbsp; volume &nbsp;= {33},    <br> &nbsp;&nbsp;&nbsp; number &nbsp;= {2},    ]]></body>
<body><![CDATA[<br> &nbsp;&nbsp;&nbsp; pages &nbsp; = {219-231}    <br> }</font></code>  <hr size="1"> </font>      ]]></body><back>
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