2

Does it makes sense to say that:

In a binomial distribution we looking for the number of successes in a given number if trials, and in a negative binomial distribution we are looking for the number of trials until a given number of (edit:) successes are achieved?

Thanks

Akiva Kahn
  • 33
  • 3
  • Does this answer your question? [Negative binomial distribution vs binomial distribution](https://stats.stackexchange.com/questions/176034/negative-binomial-distribution-vs-binomial-distribution) – Marco Plebani Jun 10 '21 at 11:44

1 Answers1

1

Better to say that in a negative binomial distribution we are looking for the number of trials until a given number of successes are achieved.

But there are four possible definitions in use:

  • number of failures until a given number of successes are achieved; with support $\{0,1,2,3,\ldots\}$ and mean $\frac{1-p}{p}r$

  • number of trials until a given number of successes are achieved; with support $\{r,r+1,r+2,\ldots\}$ and mean $\frac{1}{p}r$

  • number of successes until a given number of failures are achieved; with support $\{0,1,2,3,\ldots\}$ and mean $\frac{p}{1-p}r$

  • number of trials until a given number of failures are achieved; with support $\{r,r+1,r+2,\ldots\}$ and mean $\frac{1}{1-p}r$

Henry
  • 30,848
  • 1
  • 63
  • 107