Distribuição log-gama multivariada generalizada

Na teoria da probabilidade e estatística, a distribuição log-gama multivariada generalizada (G-MVLG)  é uma distribuição multivariada introduzidas pela Demirhan e Hamurkaroglu[1] em 2011. O G-MVLG é uma distribuição flexível. A assimetria e curtose são bem controladas pelos parâmetros da distribuição. Isso permite que uma controle a dispersão da distribuição. Devido a esta propriedade, a distribuição é usada efetivamente como um conjunto prévio de distribuição na análise Bayesiana, especialmente quando a probabilidade não é a localização-escala da família de distribuições, tais como a distribuição normal.

Função de densidade de probabilidade conjunta

Se função de densidade de probabilidade (pdf) de é dado como o seguinte:

onde para e é a correlação entre e, e indicar determinante e o valor absoluto do interior expressão, respectivamente, e inclui parâmetros da distribuição.

Propriedades

Função de geração momento conjuntos

A articulação momento em função de geração do G-MVLG de distribuição é a seguinte:

Momentos marginal central

marginal momento central de é como o seguinte:

Valor esperado e variância marginal

Valor marginal esperado é como o seguinte:

onde e são valores de digamma e trigamma funções em, respectivamente.

Distribuições relacionadas

Demirhan e Hamurkaroglu estabelecer uma relação entre o G-MVLG de distribuição e a distribuição de Gumbel (tipo I valor extremo de distribuição) e dá um multivariada forma da distribuição de Gumbel, a saber, a generalizada multivariada Gumbel (G-MVGB) de distribuição. A função de densidade de probabilidade conjunta de é o seguinte:

A distribuição de Gumbel tem uma ampla gama de aplicações no campo de análise de risco. Portanto, o G-MVGB de distribuição deve ser benéfico quando é aplicada a esses tipos de problemas..

Referências

  1. «On a multivariate log-gamma distribution and the use of the distribution in the Bayesian analysis». Journal of Statistical Planning and Inference. 141. doi:10.1016/j.jspi.2010.09.015 

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