From negative binomial to Poisson distribution

When the parameter size is +Inf, then dnbinom(x, mu, size=+Inf) is similar to dpois(x, lambda=mu):

> dnbinom(1:20, mu=5, size=+Inf)
 [1] 3.368973e-02 8.422434e-02 1.403739e-01 1.754674e-01 1.754674e-01 1.462228e-01
 [7] 1.044449e-01 6.527804e-02 3.626558e-02 1.813279e-02 8.242177e-03 3.434240e-03
[13] 1.320862e-03 4.717363e-04 1.572454e-04 4.913920e-05 1.445271e-05 4.014640e-06
[19] 1.056484e-06 2.641211e-07
> dpois(1:20, lambda =5)
 [1] 3.368973e-02 8.422434e-02 1.403739e-01 1.754674e-01 1.754674e-01 1.462228e-01
 [7] 1.044449e-01 6.527804e-02 3.626558e-02 1.813279e-02 8.242177e-03 3.434240e-03
[13] 1.320862e-03 4.717363e-04 1.572454e-04 4.913920e-05 1.445271e-05 4.014640e-06
[19] 1.056484e-06 2.641211e-07

 This is logical from the definition of variance of negative binomial distribution:

 variance = mu + mu^2 / size

 When size is +Inf, variance is mu... and then negative binomial is a Poisson distribution.

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