Multivariate Hypergeometric Distribution

Distribution$P(Y_1=y_1,Y_2=y_2,...,Y_k=y_k)=\frac{\left(\genfrac{}{}{0ex}{}{m_1}{y_1}\right)\left(\genfrac{}{}{0ex}{}{m_2}{y_2}\right)...\left(\genfrac{}{}{0ex}{}{n_k}{y_k}\right)}{\left(\genfrac{}{}{0ex}{}{N}{n}\right)}$

where:

• 𝑁 is the total number of ALL elements in the population dataset
• 𝑛 is the total number of ALL elements in the sample dataset
• 𝑚_𝑖 is the number of element 𝑖 in the population dataset
  • ${\sum }_{i=0}^k{m}_i=N$
• 𝑦_𝑖 is the number of element 𝑖 in the sample dataset
  • ${\sum }_{i=0}^k{y}_i=n$
• () is combinations without replacement