<?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>1794-6190</journal-id>
<journal-title><![CDATA[Earth Sciences Research Journal]]></journal-title>
<abbrev-journal-title><![CDATA[Earth Sci. Res. J.]]></abbrev-journal-title>
<issn>1794-6190</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1794-61902007000100001</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[GEOINFORMATION DENSITY:: A criterion on ANH Block Negotiation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Vargas J.]]></surname>
<given-names><![CDATA[Carlos A.]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Zamora R.]]></surname>
<given-names><![CDATA[Armando]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pardo]]></surname>
<given-names><![CDATA[Andres]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Agencia Nacional de Hidrocarburos  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidad Nacional de Colombia, Sede Bogotá Departamento de Geociencias ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<aff id="A03">
<institution><![CDATA[,Universidad de Caldas Departamento de Geología ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2007</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2007</year>
</pub-date>
<volume>11</volume>
<numero>1</numero>
<fpage>5</fpage>
<lpage>19</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S1794-61902007000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S1794-61902007000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S1794-61902007000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Based on the general information included within the ANH Exploration and Production Information Service, the information distribution densities of the Colombian territory were determined. These densities are referred in seismic length per square kilometer and amounts in magnetic-gravimetric and geochemical information data or drill-hole length per sq. km. A probabilistic distribution was assessed along the density distribution and cost distribution for each variable. The variables, as information layers, were cross-referenced in order to define relative weights that assess information with respect to the presence or absence of information in the treated area. This procedure could be regarded as a methodological support proposal for area negotiation of the oil industry. A better approach to the quandary should include: new input of data into the system, a division of the territory in smaller areas adjusting to complex geometries, and considering the particular market conditions for each basin. Nevertheless, it is apparent that the obtained results favor the consolidation of a conceptual framework that at medium term will allow a conscious approach towards block negotiation between the petroleum industry and the ANH.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[La clasificación automática de señales sísmicas se ha llevado a cabo típicamente sobre representaciones El uso de la información de carácter general incluida dentro del Servicio Informativo de la Exploración y de la Producción de ANH permitió la determinación de densidades de distribución de información del territorio colombiano. Estas densidades se refieren a longitud de sísmica por el kilómetro cuadrado, cantidades de datos de información magnético-gravimétrica y geoquímica, así como longitud de perforación por kilómetro cuadrado. Una distribución probabilística fue entonces estimada para la distribución de la densidad y de la distribución de costos para cada variable. Las variables como capas de información fueron pesadas relativamente para determinar la presencia o ausencia de la información en el área tratada. Este procedimiento se podría mirar como una propuesta metodológica para la ayuda en la negociación de áreas de interés en la industria del petróleo. Un acercamiento mejor al problema debería incluir: nueva entrada de datos en el sistema; una división del territorio en áreas más pequeñas que se ajusten a las geometrías complejas; y considerar las condiciones de mercado particulares en cada cuenca. Sin embargo, es evidente que los resultados obtenidos favorecen la consolidación de un marco conceptual que en el mediano plazo permitirá un acercamiento consciente hacia la negociación de bloques de interés exploratorio para la industria petrolera y la ANH.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Density of Information]]></kwd>
<kwd lng="en"><![CDATA[Oil Exploration]]></kwd>
<kwd lng="en"><![CDATA[Negotiation]]></kwd>
<kwd lng="en"><![CDATA[Colombia]]></kwd>
<kwd lng="es"><![CDATA[Densidad de Información]]></kwd>
<kwd lng="es"><![CDATA[Exploración de Petróleo]]></kwd>
<kwd lng="es"><![CDATA[Negociación]]></kwd>
<kwd lng="es"><![CDATA[Colombia]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[  <font face="verdana" size="2">      <p align="center"><font size="4"><b>GEOINFORMATION DENSITY: A criterion on ANH    Block Negotiation</b></font></p>     <p align="center"><b>Carlos A. Vargas J.1,<sup>2</sup> - Armando Zamora R. <sup>1</sup> - Andres Pardo <sup>1,3</sup></b></p>     <p><sup>1</sup> Agencia Nacional de Hidrocarburos - ANH    <br>   <sup>2</sup> Departamento de Geociencias, Universidad Nacional de Colombia - Sede  Bogot&aacute;    <br> <sup>3</sup> Departamento de Geolog&iacute;a, Universidad de Caldas</p>     <p>Corresponding author: Carlos A. Vargas J., e-mail:<a href="mailto:cavargasj@unal.edu.co">cavargasj@unal.edu.co</a></p>     <p align="center">Manuscript received March 13 2007. Accepted for publication June 20 2007.</p> <hr size="1">     <p><b>ABSTRACT</b></p>     <p>Based on the general information included within the ANH Exploration and Production    Information Service, the information distribution densities of the Colombian    territory were determined. These densities are referred in seismic length per    square kilometer and amounts in magnetic-gravimetric and geochemical information    data or drill-hole length per sq. km. A probabilistic distribution was assessed    along the density distribution and cost distribution for each variable. The    variables, as information layers, were cross-referenced in order to define relative    weights that assess information with respect to the presence or absence of information    in the treated area.</p>     ]]></body>
<body><![CDATA[<p>This procedure could be regarded as a methodological support proposal for area    negotiation of the oil industry. A better approach to the quandary should include:    new input of data into the system, a division of the territory in smaller areas    adjusting to complex geometries, and considering the particular market conditions    for each basin. Nevertheless, it is apparent that the obtained results favor    the consolidation of a conceptual framework that at medium term will allow a    conscious approach towards block negotiation between the petroleum industry    and the ANH.</p>     <p><b>Key words:</b> Density of Information, Oil Exploration, Negotiation, Colombia.</p> <hr size="1">     <p><b>RESUMEN</b></p>     <p>La clasificaci&oacute;n autom&aacute;tica de se&ntilde;ales s&iacute;smicas    se ha llevado a cabo t&iacute;picamente sobre representaciones El uso de la    informaci&oacute;n de car&aacute;cter general incluida dentro del Servicio Informativo    de la Exploraci&oacute;n y de la Producci&oacute;n de ANH permiti&oacute; la    determinaci&oacute;n de densidades de distribuci&oacute;n de informaci&oacute;n    del territorio colombiano. Estas densidades se refieren a longitud de s&iacute;smica    por el kil&oacute;metro cuadrado, cantidades de datos de informaci&oacute;n    magn&eacute;tico-gravim&eacute;trica y geoqu&iacute;mica, as&iacute; como longitud    de perforaci&oacute;n por kil&oacute;metro cuadrado. Una distribuci&oacute;n    probabil&iacute;stica fue entonces estimada para la distribuci&oacute;n de la    densidad y de la distribuci&oacute;n de costos para cada variable. Las variables    como capas de informaci&oacute;n fueron pesadas relativamente para determinar    la presencia o ausencia de la informaci&oacute;n en el &aacute;rea tratada. </p>     <p>Este procedimiento se podr&iacute;a mirar como una propuesta metodol&oacute;gica    para la ayuda en la negociaci&oacute;n de &aacute;reas de inter&eacute;s en    la industria del petr&oacute;leo. Un acercamiento mejor al problema deber&iacute;a    incluir: nueva entrada de datos en el sistema; una divisi&oacute;n del territorio    en &aacute;reas m&aacute;s peque&ntilde;as que se ajusten a las geometr&iacute;as    complejas; y considerar las condiciones de mercado particulares en cada cuenca.    Sin embargo, es evidente que los resultados obtenidos favorecen la consolidaci&oacute;n    de un marco conceptual que en el mediano plazo permitir&aacute; un acercamiento    consciente hacia la negociaci&oacute;n de bloques de inter&eacute;s exploratorio    para la industria petrolera y la ANH.</p>     <p><b>Palabras claves:</b> Densidad de Informaci&oacute;n, Exploraci&oacute;n    de Petr&oacute;leo, Negociaci&oacute;n, Colombia.</p> <hr size="1">     <p><font size="3"><b>INTRODUCTION</b></font></p>     <p>A negotiation is a communication framework where the assessed object considers    an interaction between value estimations of each participating transaction party.    This practice may become subjective, as each participant may imprint a differential    value based on its own cognizance. Evidently, he who has the utmost knowledge    of the object will have a better position to assess the cost - benefit relationship    and go appropriately further in the negotiation.</p>     <p>The strategy is to set up a large sum of negotiation criteria to establish    block allocation mechanisms within the practice of exploratory promotion developed    by the ANH. One of these criteria may be supported on the hypothesis of geoinformation    density, that is, &quot;the possibility that information distributed in a specific    area may be considered as typical and a criterion to quantify its relative investment&quot;.    Accepting this statement as starting point, it can be demonstrated that geological,    geophysical, geochemical, and in general all geospatial information, may be    conceived as an objective tool for block appraisement. In this line of thought,    the goal of this paper is guided towards defining a conceptual tool that will    allow supplementing block negotiation undertaken by the ANH within its mission    outline.</p>     <p>METHODOLOGICAL ASPECTS Based on the general information included within the    ANH Exploration and Production Information Service - EPIS such as longitude    and location of several seismic programs, gravimetric, magnetometric, and geochemical    location coverage along with well distribution performed during the exploratory    history of Colombia, information distribution densities have been determined    from territory area discretization (e.g., 25km x 25km). These densities are    referred in seismic length per square kilometer and magnetic-gravimetric and    geochemical information data amounts or drillhole length per square kilometer.</p>     ]]></body>
<body><![CDATA[<p>Once the information densities have been established for the area, the probabilistic    distribution is assessed along with the inferred relative weighing factors to    the density distribution and cost distribution for each variable. The variables,    as information layers, have been cross-referenced in order to define relative    weights that assess information weighters with respect to the presence or absence    of information in each treated area. <a href="img/revistas/esrj/v11n1/v11n1a01f01.gif" target="_blank">Figure 1</a> depicts a synthetic outline establishing    the procedures followed on this paper.</p>     <p>DATA It could be stated that a number of the geospatial variables analyzed    show strong contrasts with respect to their distribution in Colombia. <a href="#Figure 2">Figure 2</a>     shows the location of seismic information depicting a dense coverage towards    the Eastern plains (Llanos Orientales) basin including the Eastern Mountain    Range foothills, Putumayo and Magdalena Valley (high, medium, and low), Pacific    off-shore coast (central and south region), Atlantic off-shore coast, and Sin&uacute;-San    Jacinto and Cesar-Rancher&iacute;a basins. In contrast, low information densities    are seen towards the Orinoqu&iacute;a and Amazon regions, north of the Department    of Choc&oacute;, and along the mountain range axis. A similar situation is seen    with the magnetic and gravimetric information, well distribution, and geochemical    controls (<a href="#Figures 3">Figures 3</a>, <a href="#4">4</a>, and <a href="#5">5</a>).</p>     <p>    <center><a name="Figure 2"><img src="img/revistas/esrj/v11n1/v11n1a01f02.gif"></a></center></p>     <p>    <center><a name="Figures 3"><img src="img/revistas/esrj/v11n1/v11n1a01f03.gif"></a></center></p>     <p>    <center><a name="4"><img src="img/revistas/esrj/v11n1/v11n1a01f04.gif"></a></center></p>     <p>    <center><a name="5"><img src="img/revistas/esrj/v11n1/v11n1a01f05.gif"></a></center></p>     ]]></body>
<body><![CDATA[<p>Even though the EPIS database has information voids in some periods and there    are time differences in data entry in the same database, probably as a testimony    of the change of administration, its current structure and contents remains    representative and may guarantee that the database is suitable to assess the    exploratory tendencies and ensure an appropriate criterion for block negotiation.</p>     <p><b>ANALYSIS AND RESULTS DISTRIBUTION FUNCTION</b></p>     <p>To understand how spatial distribution of geoinformation density could be analyzed,    it is necessary to begin from an analysis of the distribution function that    better suits the observations. For instance, seismic density registered in Colombia    could be used as a representative variable for this procedure. <a href="img/revistas/esrj/v11n1/v11n1a01f06.gif" target="_blank">Figure 6</a> shows    the distribution of density frequencies and the best fit representing two models    of statistical distribution: Normal and Gamma. For the first event, a strong    unbalance is seen, suggesting that the distribution could not comply with a    normal distribution process.</p>     <p>Usually, offer and demand processes follow normal distributions. In this event,    although it is a similar scenario for area allocation, it follows a Gamma pattern    fit, specifically an exponential distribution (Ayyub and McCuen, 2003). Exponential    distributions are useful to assess processes through time (Blaesid and Granfeldt,    2003). However, this condition is not reflected in our issue because this is    a data set encompassing the whole observation period, and illustrates a scenario    where the main biasing frequency almost dominates the distribution below the    mode and in turn allows values greater than frequency. A checkmark for this    distribution may be seen in the simple and cumulative probability curves (<a href="img/revistas/esrj/v11n1/v11n1a01f07.gif" target="_blank">Figures 7</a> and <a href="img/revistas/esrj/v11n1/v11n1a01f08.gif" target="_blank">8</a>). The behavior is similar to &quot;club admittance&quot;, in other    words there is a minimum fee to be a member, but any sum above the minimum is    also admissible and very exceptionally members below the fee will be presented.</p>     <p>This is situation fundamentally imposed by the petroleum industry, which possibly    will promote increases in admission quotas when the business tends to be more    attractive. In effect, for a greater observation time and under the same energy    requirements in Colombia, it could be expected that the seismic information    density as a criterion for block allocation (admission quota) tends to be greater.    <a href="#Table 1">Table 1</a> shows the parameters for each distribution.</p>     <p>    <center><a name="Table 1"><img src="img/revistas/esrj/v11n1/v11n1a01t01.gif"></a></center></p>     <p>A similar situation is seen in distribution functions for information densities    associated to the amount of magneto-gravimetric points and drill-hole length    (<a href="img/revistas/esrj/v11n1/v11n1a01f09.gif" target="_blank">Figures 9</a> and <a href="img/revistas/esrj/v11n1/v11n1a01f10.gif" target="_blank">10</a>). For well data (m/km2), this index depicts in certain degree,    the inversion rate executed to know a given area. Likewise, information density    related with the number of geochemical stations should take into account the    dissimilarity in the level of tests for each station (TOC, pyrolysis, organic    petrography, sulphur content, metal content, rock extracci&oacute;n, liquid    gas chromatography, and biomarkers). This information is conditioned to the    existence of an analysis sequence protocol as a function of the results obtained    from certain initial testing such as TOC and Pyrolysis. Therefore, its representability    only grants a partial nature (<a href="img/revistas/esrj/v11n1/v11n1a01f11.gif" target="_blank">Figure 11</a>). A representation of these variables    in the Colombian territory is shown in density information maps associated with    the analyzed variables (<a href="img/revistas/esrj/v11n1/v11n1a01f12.gif" target="_blank">Figures 12</a>, <a href="img/revistas/esrj/v11n1/v11n1a01f13.gif" target="_blank">13</a>, <a href="img/revistas/esrj/v11n1/v11n1a01f14.gif" target="_blank">14</a>, and <a href="img/revistas/esrj/v11n1/v11n1a01f15.gif" target="_blank">15</a>).</p>     <p><a href="img/revistas/esrj/v11n1/v11n1a01t02.gif" target="_blank">Table 2</a> summarizes the exponential distribution parameters converted into relative    weights, describing all the observed information. Generally, empirical adjustments    with confidence levels can be seen, widely reproducing the behavior for the    amount of data for the observed period.</p>     <p><b>ESTIMATION OF A RELATIVE WEIGHTING FACTOR FOR AREA NEGOTIATION</b></p>     ]]></body>
<body><![CDATA[<p> The exponential probability distribution function and probability estimation    have been defined as (Blaesid and Granfeldt, 2003):</p>     <p>where &micro; is the arithmetic mean and x the discrete value of the distribution    of the estimated probability. For all previously analyzed information densities,    it is necessary to shorten the <a href="#equation02">equation (2)</a> to a relative weight factor that    promotes the generation of new knowledge in areas where data is scarce:</p>     <p align="center"><a name="equation02"><img src="img/revistas/esrj/v11n1/v11n1a01e02.gif"></a></p>     <p>The weighting factor (<i>w</i>) is a tool that relatively contemplates initiatives    directed towards new surveys under different block contracting employed by ANH.    According to <a href="#equation03">equation (3)</a>, areas with plenty of information will be penalized    with low weighting factors and viceversa. Obviously, upon promoting strategies    encouraging enforcement of new scientific and technological procedures on areas    of interest, the need to estimate other weighting factors with the <a href="#equation03">equation    (3)</a> is a must.</p>     <p align="center"><a name="equation03"><img src="img/revistas/esrj/v11n1/v11n1a01e03.gif"></a></p>     <p><b>INFORMATION LAYER WEIGHTING</b></p>     <p>As can be expected, the relative sum of related weights with all variables,    allows having an approach to the spatial distribution of information density.    Although average costs for each variable are very different and entail another    relative weighting to market averages. <a href="#Table03">Table 3</a> shows Colombian seismic kilometer    average costs, unitary values for each magneticgravimetric and geochemical point    and linear drill-hole foot (with more frequent analyses), as developed approximate    amounts. It could be seen that seismic is the most expensive exploratory variable,    apart from being the most widely used. Likewise, the technical link between    seismics and wells is noticeable, being these two representable variables of    areas where the major exploration investments have been executed.Therefore,    superimposing the drill-hole density map on top of the seismic density information    map, or at least one of these two variables, may be a criterion enough to estimate    a map of information density relative to the weighting providing support for    block negotiation processes.</p>     <p align="center"><a name="Table03"><img src="img/revistas/esrj/v11n1/v11n1a01t03.gif"></a></p>     <p>Nevertheless, <a href="#equation04">equation 4</a> is an empirical approach that assumes the superimposition    of all variables taken into consideration and weighting the relative cost of    each variable.</p>     <p align="center"><a name="equation04"><img src="img/revistas/esrj/v11n1/v11n1a01e04.gif"></a></p>     ]]></body>
<body><![CDATA[<p>The estimates seen in <a href="#equation04">equation (4)</a> enabled performing a weighted geoinformation    density map (<a href="img/revistas/esrj/v11n1/v11n1a01f16.gif" target="_blank">Figure 16</a>). This map highlights the areas where the effect of new    exploratory information has less effect. Possibly, the current setting may vary    as new data is added to the information foundation that engineered it.</p>     <p>According to <a href="img/revistas/esrj/v11n1/v11n1a01f16.gif" target="_blank">Figure 16</a>, there are areas where no exploratory efforts have been    undertaken as those analyzed, namely those in the Colombian eastern border,    the borders with Venezuela and Brazil, in the Serran&iacute;a of San Lucas,    the Junction of the Pastos, the Sierra Nevada of Santa Marta, and the lower    Cauca river valley. This state of affairs can be explained in view of the current    geological knowledge. These areas do not seem to be favored by their inherent    geological conditions and possibly have no mineral-energy potential of interest.    In contrast, some areas have vast amounts of information density, evidenced    by the widespread of exploratory activity such as the Eastern plains, Putumayo,    and the Magdalena Mid-Valley.</p>     <p>On the other hand, some belts and areas with high information density are suddenly    interrupted making it uncertain to know the potential continuity of the prospects    that have not been adequately analyzed as the northern part of the pacific coast    and towards the north of Putumayo. Although it is necessary to further analyze    the information densities of these areas, it is also clear that the socio-environmental    conditions of these areas are intricate and have hindered the possible development    of potential prospects.</p>     <p><font size="3"><b>CONCLUSIONS</b></font></p>     <p>The development of the present knowledge management assignment based on the    EPIS database should be regarded as a methodological support proposal for area    negotiation whose quantitative results rise above the preliminary results. A    better approach to the dilemma should include:</p>     <p>1. New input of data into the system as a consequence of an exhaustive search    of data to complement the current petroleum knowledge of the country. 2. The    discretization of the territory in smaller areas adjusted to complex geometry,    showing the current conditions for block negotiation. 3. An approach of the    problem considering the particular market conditions for each basin. 4. Data    entry that establishes new information layers allowing to improve the relative    weighting of geoinformation such as seismic information reprocessing and dating.    5. Breaking up information in basic data that allows to establish information    layers with differing weights (e.g., differentiation of stratigraphic wells    into different diameters and considering supplementary surveys such as electrical    registry and petrophysical testing).</p>     <p>Nevertheless, it is apparent that the obtained results favor the consolidation    of a conceptual framework that at medium term will allow a conscious approach    towards block negotiation between the petroleum industry and the ANH.</p>     <p><font size="3"><b>ACKNOWLEDGMENTS</b></font></p>     <p>To the staff at Schlumberger, particularly to Edgar Medina and Liliana Salcedo,    for enduring two months of my intense requirements over the available EPIS system    information.</p>     <p><font size="3"><b>REFERENCES</b></font></p>     ]]></body>
<body><![CDATA[<!-- ref --><p>1. Ayyub, B.M. and McCuen, R.H. (2003). Probability, statistics, and reliability    for engineers and scientists. New York: Chapman &amp; Hall/CRC Press.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000063&pid=S1794-6190200700010000100001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>2. Balakrishnan, N. and Basu, A. P. (1996). The Exponential Distribution: Theory,    Methods, and Applications. New York: Gordon and Breach. Blaesild, P. and Granfeldt,    J. (2003). Statistics&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000064&pid=S1794-6190200700010000100002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>3. Blaesild, P. and&nbsp; Granfeldt, J. (2003). Statistics with applications in biology and geology. New York: Chapman &amp; Hall/CRC Press.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000065&pid=S1794-6190200700010000100003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p>4. Spiegel, M. R. (1992). Theory and Problems of Probability and Statistics.    New York: McGraw- Hill, p. 119. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000066&pid=S1794-6190200700010000100004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
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<given-names><![CDATA[P.]]></given-names>
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<name>
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<given-names><![CDATA[J.]]></given-names>
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<source><![CDATA[Statistics with applications in biology and geology]]></source>
<year>2003</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Chapman & Hall/CRC Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Spiegel]]></surname>
<given-names><![CDATA[M. R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Theory and Problems of Probability and Statistics]]></source>
<year>1992</year>
<page-range>119</page-range><publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[McGraw- Hill]]></publisher-name>
</nlm-citation>
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</ref-list>
</back>
</article>
