Negative Binomial Distribution in R Programming

Question

Why do I get a different answer when I use the density function?

pnbinom(3,2,.5)
#[1] 0.8125

a=dnbinom(5,0,0.5)+dnbinom(4,1,.5)+dnbinom(3,2,.5)
a
#[1] 0.15625

Answer 1

You can try this:

pnbinom(3,2,0.5)

sum(dnbinom(0:3,2,0.5))

Here's the output:

> pnbinom(3,2,0.5)
[1] 0.8125
> 
> sum(dnbinom(0:3,2,0.5))
[1] 0.8125