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Seja X uma variável aleatória, e E() o operador esperança. Então os cumulantes são definidos através da expansão em série de Taylor de log⁡(E(exp⁡(tX))){displaystyle log(E(exp(tX))),}{displaystyle log(E(exp(tX))),}, ou seja:


g(t)=log⁡(E(exp⁡(tX)))=∑n=1∞κntnn!=μt+σ2t22+⋯{displaystyle g(t)=log(Eleft(exp(tX)right))=sum _{n=1}^{infty }{frac {kappa _{n}t^{n}}{n!}}=mu t+{frac {sigma ^{2}t^{2}}{2}}+cdots ,}{displaystyle g(t)=log(Eleft(exp(tX)right))=sum _{n=1}^{infty }{frac {kappa _{n}t^{n}}{n!}}=mu t+{frac {sigma ^{2}t^{2}}{2}}+cdots ,}

Como casos particulares, κ1{displaystyle kappa _{1},}{displaystyle kappa _{1},} é a média e κ2{displaystyle kappa _{2},}{displaystyle kappa _{2},} é a variância.





Ícone de esboço Este artigo sobre matemática é um esboço. Você pode ajudar a Wikipédia expandindo-o.



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