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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
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1 Answers1

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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
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