<?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>S0120-17512006000100001</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una estimación del parámetro de la distribución g de Tukey]]></article-title>
<article-title xml:lang="en"><![CDATA[An Estimation of the Parameter of the g Tukey Distribution]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[JIMÉNEZ]]></surname>
<given-names><![CDATA[JOSÉ ALFREDO]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[MARTÍNEZ]]></surname>
<given-names><![CDATA[JORGE]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de Matemáticas ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Nacional de Colombia Departamento de EstadÍstica ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>03</day>
<month>06</month>
<year>2006</year>
</pub-date>
<pub-date pub-type="epub">
<day>03</day>
<month>06</month>
<year>2006</year>
</pub-date>
<volume>29</volume>
<numero>1</numero>
<fpage>1</fpage>
<lpage>16</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-17512006000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-17512006000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-17512006000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Se presenta una forma explícita de la función de densidad de una variable con distribución g-h de Tukey, en términos de los cuantiles de la distribución normal estándar. La expresión de la densidad de probabilidad propuesta permite establecer un estimador del parámetro g asociado a la subfamilia de distribuciones g de Tukey.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[This paper presents an explicit form of the density function of a random variable with the g-h Tukey distribution, in terms of the quantiles of the standard normal distribution. The estimator of the parameter g is obtained based on this particular form of the probability density.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Cuantiles]]></kwd>
<kwd lng="es"><![CDATA[distribución g-h de Tukey]]></kwd>
<kwd lng="en"><![CDATA[Quantiles]]></kwd>
<kwd lng="en"><![CDATA[g-h Tukey distribution]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[   <font size="2" face="verdana">        <p>    <center><b><font size="4">Una estimación del parámetro de la distribución  g de Tukey</font></b></center></p>        <p>    <center><b><font size="3">An Estimation of the Parameter of the g Tukey Distribution</font></b></center></p>        <p>    <center>JOS&Eacute; ALFREDO JIM&Eacute;NEZ<sup>1</sup>, JORGE MART&Iacute;NEZ<sup>2</sup></center></p>        <p><sup>1</sup>Universidad Nacional de Colombia, Bogotá, Profesor asociado, Departamento de Matemáticas. E-mail: <a href="mailto:josajimenezm@unal.edu.co">josajimenezm@unal.edu.co</a>    <br>  <sup>2</sup>Universidad Nacional de Colombia, Bogotá, Profesor asociado, Departamento de Estad&Iacute;stica. E-mail: <a href="mailto:jmartinezc@unal.edu.co">jmartinezc@unal.edu.co</a></p>    <hr size="1">        <p><b>    ]]></body>
<body><![CDATA[<center>Resumen</center></b></p>        <p>Se presenta una forma expl&iacute;cita de la funci&oacute;n de densidad de una variable  con distribuci&oacute;n <i>g-h</i> de Tukey, en t&eacute;rminos de los cuantiles de la distribuci&oacute;n normal est&aacute;ndar. La expresi&oacute;n de la densidad de probabilidad propuesta  permite establecer un estimador del par&aacute;metro g asociado a la subfamilia de  distribuciones <i>g</i> de Tukey.</p>        <p><i><b>Palabras clave:</b></i> Cuantiles, distribuci&oacute;n <i>g-h</i> de Tukey.</p>    <hr size="1">        <p><b>    <center>Abstract</center></b></p>        <p>This paper presents an explicit form of the density function of a random  variable with the <i>g-h</i> Tukey distribution, in terms of the quantiles of the  standard normal distribution. The estimator of the parameter <i>g</i> is obtained  based on this particular form of the probability density.</p>        <p><b><i>Key words:</i></b> Quantiles, <i>g-h</i> Tukey distribution.</p>    <hr size="1">        <p>Texto completo disponible en <a href="pdf/rce/v29n1/v29n1a01.pdf">PDF</a></p>    <hr size="1">        <p><b><font size="3">Referencias</font></b></p>        <!-- ref --><p>1. Apostol, T. M. (1985), <i>Calculus</i>, Vol. I, Editorial Revert&eacute; S.A., Barcelona.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000022&pid=S0120-1751200600010000100001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>2. Caballero, G. (1986), Un estimador del par&aacute;metro <i>g</i> de la distribuci&oacute;n <i>g</i> de Tukey,  Tesis de maestr&iacute;a (estad&iacute;stica), Universidad Nacional de Colombia, Facultad  de Ciencias. Departamento de Estad&iacute;stica. Bogot&aacute;.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000023&pid=S0120-1751200600010000100002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>3. Herazo, C. A. (1984), Distribuci&oacute;n g¡h de Tukey y aplicaciones a las distribuciones  de vida, Tesis de maestr&iacute;a (estad&iacute;stica), Universidad Nacional de Colombia,  Facultad de Ciencias. Departamento de Estad&iacute;stica. Bogot&aacute;.&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=S0120-1751200600010000100003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>4. Hoaglin, D., Mosteller, F. & Tukey, J. (1985), <i>Exploring Data Tables, Trends, and  Shapes</i>, John Wiley & Sons, Inc., USA.&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=S0120-1751200600010000100004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>5. Hoaglin, D. & Peters, S. (1979), &quot;Software for exploring distribution shape&quot;, <i>Pro  ceedings of computer science and statistics</i>.&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=S0120-1751200600010000100005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>6. Jim&eacute;nez, J. A. (2004), Aproximaciones de las funciones de riesgo del tiempo de  sobrevivencia mediante la distribuci&oacute;n <i>g-h</i> de Tukey, Trabajo de grado (Es-  pecializaci&oacute;n en Actuar&iacute;a), Universidad Nacional de Colombia, Facultad de  Ciencias. Departamento de Matem&aacute;ticas. Bogot&aacute;.&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=S0120-1751200600010000100006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>7. Lee, E. T. (1992), <i>Statistical Methods for Survival Data Analysis</i>, second edn, John  Wiley & Sons, Inc., 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=S0120-1751200600010000100007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>8. Mart&iacute;nez, J. (1981), <i>Some Applications of Robust Scale Estimators</i>, Doctoral The-  sis, Temple University, Department of Statistics. Philadelphia.&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=S0120-1751200600010000100008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>9. Mart&iacute;nez, J. & Iglewicz, B. (1984), &quot;Some properties of the Tukey g and h family of  distributions&quot;,<i>Communications in Statistics: Theory and Methods</i> <b>13</b>(3), 353-  369.&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=S0120-1751200600010000100009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>10. Tukey, J. (1977), <i>Exploratory Data Analysis</i>, Reading, MA: Addison-Wesley, USA.&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=S0120-1751200600010000100010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Apostol]]></surname>
<given-names><![CDATA[T. M]]></given-names>
</name>
</person-group>
<source><![CDATA[Calculus]]></source>
<year>1985</year>
<volume>I</volume>
<publisher-loc><![CDATA[Barcelona ]]></publisher-loc>
<publisher-name><![CDATA[Editorial Reverté S.A]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Caballero]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<source><![CDATA[Un estimador del parámetro g de la distribución g de Tukey]]></source>
<year>1986</year>
</nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herazo]]></surname>
<given-names><![CDATA[C. A]]></given-names>
</name>
</person-group>
<source><![CDATA[Distribución g¡h de Tukey y aplicaciones a las distribuciones de vida]]></source>
<year>1984</year>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hoaglin]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
<name>
<surname><![CDATA[Mosteller]]></surname>
<given-names><![CDATA[F]]></given-names>
</name>
<name>
<surname><![CDATA[Tukey]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Exploring Data Tables, Trends, and Shapes]]></source>
<year>1985</year>
<publisher-name><![CDATA[John Wiley & Sons, Inc]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hoaglin]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
<name>
<surname><![CDATA[Peters]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[&lsquo; Software for exploring distribution shape&rsquo;]]></article-title>
<source><![CDATA[Pro ceedings of computer science and statistics]]></source>
<year>1979</year>
</nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jiménez]]></surname>
<given-names><![CDATA[J. A]]></given-names>
</name>
</person-group>
<source><![CDATA[Aproximaciones de las funciones de riesgo del tiempo de sobrevivencia mediante la distribución g-h de Tukey]]></source>
<year>2004</year>
</nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lee]]></surname>
<given-names><![CDATA[E. T]]></given-names>
</name>
</person-group>
<source><![CDATA[Statistical Methods for Survival Data Analysis]]></source>
<year>1992</year>
<edition>second</edition>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley & Sons, Inc]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Some Applications of Robust Scale Estimators]]></source>
<year>1981</year>
</nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Iglewicz]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[&lsquo; Some properties of the Tukey g and h family of distributions&rsquo;]]></article-title>
<source><![CDATA[Communications in Statistics: Theory and Methods]]></source>
<year>1984</year>
<volume>13</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>353- 369</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tukey]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Exploratory Data Analysis, Reading]]></source>
<year>1977</year>
<publisher-name><![CDATA[MA: Addison-Wesley]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
