توزیع دریکله عمومی

اگر ${\displaystyle X=\left(X_1,\dots ,X_k\right)\sim G{D}_k\left({\alpha }_1,\dots ,{\alpha }_k;{\beta }_1,\dots ,{\beta }_k\right)}$

${\displaystyle E\left[X_1^{r_1}{X}_2^{r_2}\cdots X_k^{r_k}\right]=\prod _{j=1}^k\frac{\mathrm{\Gamma }\left({\alpha }_j+{\beta }_j\right)\mathrm{\Gamma }\left({\alpha }_j+r_j\right)\mathrm{\Gamma }\left({\beta }_j+{\delta }_j\right)}{\mathrm{\Gamma }\left({\alpha }_j\right)\mathrm{\Gamma }\left({\beta }_j\right)\mathrm{\Gamma }\left({\alpha }_j+{\beta }_j+r_j+{\delta }_j\right)}}$

که ${\displaystyle {\delta }_j=r_{j+1}+r_{j+2}+\cdots +r_k}$

${\displaystyle E\left(X_j\right)=\frac{{\alpha }_j}{{\alpha }_j+{\beta }_j}\prod _{m=1}^{j-1}\frac{{\beta }_m}{{\alpha }_m+{\beta }_m}.}$

1. https://web.archive.org/web/20081119000022/http://www.nscb.gov.ph/ncs/9thncs/papers/theory_Generalization.pdf