Distribuição multinomial

Em probabilidade e estatística, a distribuição multinomial é uma generalização da distribuição binomial para casos onde temos mais de dois possíveis resultados, sendo assim é uma distribuição de probabilidade discreta e multivariada.

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Temos um total de objetos/itens separados independentemente em categorias/tipos, um item é da categoria com probabilidade não-nula onde , além disso dizemos que é a quantidade de itens na categoria onde . Como se trata de um caso multivariado dizemos que o vetor aleatório tem distribuição multinomial e denotamos onde .

Função massa de probabilidade (conjunta) multinomial[1]:

Onde as reticências indicam um produtório e .

Referências

  1. Blitzstein, Joseph K. (2019). Introduction to probability. Jessica Hwang Second edition ed. Boca Raton: [s.n.] OCLC 1085348357 

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