If X is Erlang$(k_1,\lambda)$ and Y is Erlang$(k_2,\lambda)$, then is X+Y Erlang$(k_1+k_2,\lambda)$? Do X and Y need to be independent?
If X is Erlang$(k_1,\lambda)$ and Y is Erlang$(k_2,\lambda)$, then is X+Y Erlang$(k_1+k_2,\lambda)$?
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probability-distributions
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1Yes, the distributions are presumed independent in the context of that factoid. – 2011-07-09
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1Can you define or give a reference for the distribution "Erlang"? – 2011-07-09
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0@Rasmus Wikipedia http://en.wikipedia.org/wiki/Erlang_distribution will do. In summary an erlang$(k,\lambda)$ distribution is a $\Gamma(k,1/\lambda)$. It is sufficient that the erlang variables are independent. I suspect that Jim is asking whether it necessary as well. – 2011-07-09