<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332021000100105</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v28i1.12345</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Modelación predictiva de siniestros en seguros de no vida]]></article-title>
<article-title xml:lang="en"><![CDATA[Predictive Modelling of losses in non-life insurance]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sandí-Corrales]]></surname>
<given-names><![CDATA[Ana Rosa]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>07</month>
<year>2021</year>
</pub-date>
<volume>28</volume>
<numero>1</numero>
<fpage>105</fpage>
<lpage>124</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332021000100105&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332021000100105&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332021000100105&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Se analizó un seguro de accidentes y salud que tiene primas diferenciadas para grupos de riesgo homogéneos. La estimación de dichas primas en ocasiones anteriores fue de tipo univariado, que tiene la limitante de que cuando hay grupos de riesgo con pocas observaciones los resultados son muy volátiles y omiten la información que podrían aportar variables predictoras. Por lo que se optó por estimar los siniestros esperados (que son insumo del cálculo de primas) con tres modelos multivariados: lineales ordinarios, aditivos y lineales mixtos. Se utilizaron varios con el fin de comparar su capacidad de pronóstico. El desempeño fue aceptable tanto dentro de la muestra de ajuste como de prueba en el caso de los modelos lineal ordinario y aditivo con una diferencia porcentual de alrededor del 1% con respecto a los datos reales. El lineal mixto no pudo hacer pronósticos para combinaciones de predictores no observados en los datos de ajuste.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Accident and health insurance with differentiated premiums for homogeneous risk groups was analyzed. The estimation of these premiums on previous opportunities was in univariate form, which has the limitation that when there are risk groups with few observations, the results are very volatile and omit the information that could provide predictive variables. Therefore, it was decided to estimate the expected claims (which are an input in the premium calculation) with three multivariate models: ordinary linear, additive and mixed linear. Several were used in order to compare their forecasting capability. Performance was acceptable within both the fit and test samples in the case of ordinary linear and additive models with a difference of about 1% from the real data. Linear mixed could not make predictions for combinations of predictors not observed in the fit data.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[seguros]]></kwd>
<kwd lng="es"><![CDATA[tarificación]]></kwd>
<kwd lng="es"><![CDATA[modelación predictiva]]></kwd>
<kwd lng="es"><![CDATA[modelos lineales]]></kwd>
<kwd lng="es"><![CDATA[modelos aditivos]]></kwd>
<kwd lng="es"><![CDATA[modelos mixtos]]></kwd>
<kwd lng="es"><![CDATA[paquete estadístico R.]]></kwd>
<kwd lng="en"><![CDATA[insurance]]></kwd>
<kwd lng="en"><![CDATA[pricing]]></kwd>
<kwd lng="en"><![CDATA[predictive modelling]]></kwd>
<kwd lng="en"><![CDATA[linear models]]></kwd>
<kwd lng="en"><![CDATA[additive models]]></kwd>
<kwd lng="en"><![CDATA[mixed models]]></kwd>
<kwd lng="en"><![CDATA[software R.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Buja]]></given-names>
</name>
<name>
<surname><![CDATA[T]]></surname>
<given-names><![CDATA[Hastie]]></given-names>
</name>
<name>
<surname><![CDATA[R]]></surname>
<given-names><![CDATA[Tibshirani.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Linear smoothers and additive models]]></article-title>
<source><![CDATA[The Annals of Statistics]]></source>
<year>1989</year>
<volume>17</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>453-510</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Correa Morales]]></given-names>
</name>
<name>
<surname><![CDATA[J]]></surname>
<given-names><![CDATA[Salazar Uribe.]]></given-names>
</name>
</person-group>
<source><![CDATA[Introducción a los modelos mixtos]]></source>
<year>2016</year>
<publisher-loc><![CDATA[Bogotá ]]></publisher-loc>
<publisher-name><![CDATA[Universidad Nacional de Colombia]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[M]]></surname>
<given-names><![CDATA[Durbán.]]></given-names>
</name>
</person-group>
<source><![CDATA[Métodos de suavizado eficientes con P-splines]]></source>
<year>2015</year>
<publisher-loc><![CDATA[Madrid, España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad Carlos III]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[J,J]]></surname>
<given-names><![CDATA[Faraway.]]></given-names>
</name>
</person-group>
<source><![CDATA[Linear models with R]]></source>
<year>2004</year>
<numero>1</numero>
<issue>1</issue>
<publisher-loc><![CDATA[Boca Raton FL ]]></publisher-loc>
<publisher-name><![CDATA[Chapman &amp; Hall/CRC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Faraway]]></surname>
<given-names><![CDATA[J,J,]]></given-names>
</name>
</person-group>
<source><![CDATA[Extending the linear model with R: generalized linear, mixed effects and nonparametric regression]]></source>
<year>2006</year>
<numero>1</numero>
<issue>1</issue>
<publisher-loc><![CDATA[Boca Raton FL ]]></publisher-loc>
<publisher-name><![CDATA[Chapman &amp; Hall/CRC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[W,E]]></surname>
<given-names><![CDATA[Frees]]></given-names>
</name>
<name>
<surname><![CDATA[R,A]]></surname>
<given-names><![CDATA[Derrig]]></given-names>
</name>
<name>
<surname><![CDATA[G]]></surname>
<given-names><![CDATA[Meyers.]]></given-names>
</name>
</person-group>
<source><![CDATA[Predictive Modeling Applications in Actuarial Science: Predictive Modeling Techniques]]></source>
<year>2014</year>
<numero>1</numero>
<issue>1</issue>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[W,E]]></surname>
<given-names><![CDATA[Frees]]></given-names>
</name>
<name>
<surname><![CDATA[R,A]]></surname>
<given-names><![CDATA[Derrig]]></given-names>
</name>
<name>
<surname><![CDATA[G]]></surname>
<given-names><![CDATA[Meyers.]]></given-names>
</name>
</person-group>
<source><![CDATA[Predictive Modeling Applications in Actuarial Science: Case Studies in Insurance]]></source>
<year>2016</year>
<numero>2</numero>
<issue>2</issue>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[P]]></surname>
<given-names><![CDATA[Ibarrola.]]></given-names>
</name>
</person-group>
<source><![CDATA[Gauss y la estadística]]></source>
<year>2017</year>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[K,H]]></surname>
<given-names><![CDATA[Jensen.]]></given-names>
</name>
</person-group>
<source><![CDATA[Linear mixed effects models (lme)]]></source>
<year>2016</year>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[A]]></surname>
<given-names><![CDATA[Montesinos López.]]></given-names>
</name>
</person-group>
<source><![CDATA[Estudio del AIC y BIC en la selección de modelos de vida con datos censurados]]></source>
<year>2011</year>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D]]></surname>
<given-names><![CDATA[Nychka.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Splines as local smoothers]]></article-title>
<source><![CDATA[The Annals of Statistics]]></source>
<year>1995</year>
<volume>23</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1175-97</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rubalcaba]]></surname>
<given-names><![CDATA[J,G,]]></given-names>
</name>
</person-group>
<source><![CDATA[Cosas que conviene saber al usar AIC, DIC y otros criterios de información]]></source>
<year>2016</year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
