<div dir="ltr"><div style="font-size:12.8px">Estimadas e Estimados,</div><div style="font-size:12.8px"><br></div><div style="font-size:12.8px"><span style="font-size:12.8px">O Departamento de Estatística da Universidade Federal da Bahia convida a todos para prestigiar em seu Ciclo de Palestras o seminário do professor <b>Juan Carlos Arismendi Zambrano</b>, da Faculdade de Economia da Universidade Federal da Bahia.</span></div><div style="font-size:12.8px"><br></div><div style="font-size:12.8px"><p class="MsoNormal" align="center" style="margin-bottom:0.0001pt;text-align:center;background-image:initial;background-repeat:initial"><font color="#ff0000" face="Arial, sans-serif"><span style="font-size:18px"><b>Multivariate truncated moments</b></span></font><br></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:'Times New Roman',serif"> </span><span style="font-size:9.5pt;font-family:Arial,sans-serif"></span></p><p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;background-image:initial;background-repeat:initial"><b style="font-size:12.8px"><span style="font-size:13.5pt;font-family:Arial,sans-serif">Abstract</span></b><span style="font-size:13.5pt;font-family:Arial,sans-serif"> -</span><span style="font-size:12.8px"> </span><font face="Arial, sans-serif"><span style="font-size:18px">We derive formulae for the higher order tail moments of the lower truncated multivariate standard normal (MVSN), Student’s <i>t</i>, lognormal and a finite-mixture of multivariate normal distributions (FMVN). For the MVSN we propose a recursive formula for moments of arbitrary order as a generalization of previous research. For the Student’s <i>t</i>-distribution, the recursive formula is an extension of the normal case and when the degrees of freedom <i>ν</i> → ∞ the tail moments converge to the normal case. For the lognormal, we propose a general result for distributions in the positive domain. Potential applications include robust </span></font><span style="font-size:18px;font-family:Arial,sans-serif">statistics, reliability theory, survival analysis and extreme value theory. As an application of our results we calculate the exceedance skewness and kurtosis and we propose a new definition of multivariate skewness and kurtosis using tensors with the moments in their components. The tensor skewness and kurtosis captures more information about the shape of distributions than previous definitions.</span></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><font face="Arial, sans-serif"><span style="font-size:18px"><br></span></font></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><b style="font-size:12.8px"><span style="font-size:13.5pt;font-family:Arial,sans-serif">Data</span></b><span style="font-size:13.5pt;font-family:Arial,sans-serif">: 13/05/2016 (sexta-feira), às 11 horas da manhã.</span><br></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif"></span></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><b><span style="font-size:13.5pt;font-family:Arial,sans-serif">Local</span></b><span style="font-size:13.5pt;font-family:Arial,sans-serif">: Sala 15, no andar térreo do Instituto de Matemática da UFBA.</span><span style="font-size:9.5pt;font-family:Arial,sans-serif"></span></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><span style="font-size:9.5pt;font-family:Arial,sans-serif"> </span></p><p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;background-image:initial;background-repeat:initial"><font face="Arial, sans-serif" style="font-size:12.8px"><span style="font-size:18px"><b><font color="#000000">Apresentador:</font><font color="#ff0000"> </font></b></span></font><font color="#ff0000" face="Arial, sans-serif"><span style="font-size:18px"><b>Juan Carlos Arismendi Zambrano</b></span></font><br></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><font face="Arial, sans-serif"><span style="font-size:18px"></span></font></p><p class="MsoNormal" style="margin-bottom:0.0001pt;text-align:justify;background-image:initial;background-repeat:initial"><font face="Arial, sans-serif"><span style="font-size:18px">Possui graduação em Computer Engineering - Universidad Simón Bolívar, mestrado em Finance - Instituto de Estudios Superiores en Administración, mestrado em Master in Computer Science - Universidad Simon Bolivar e doutorado em Finance - University of Reading. Atualmente é professor adjunto da Faculdade de Economia da Universidade Federal da Bahia. Tem experiência na área de Probabilidade e Estatística, atuando principalmente nos seguintes temas: portfolio optimisation, risk management e higher-order moments.</span></font><br></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><font face="Arial, sans-serif"><span style="font-size:18px"><br></span></font></p><p class="MsoNormal" style="margin-bottom:0.0001pt;font-size:12.8px;text-align:justify;background-image:initial;background-repeat:initial"><font face="Arial, sans-serif"><span style="font-size:18px"><b>Coordenador</b>: Rodrigo de Souza Bulhões</span></font></p></div></div>