The negative binomial distribution is discrete. It is useful for modeling the distribution of the number of trials until the rth successful occurrence, such as the number of sales calls you need to make to close ten orders. It is essentially a super-distribution of the geometric distribution.
The negative binomial distribution is used under these conditions:
Some characteristics of the negative binomial distribution:
When Shape = 1, the negative binomial distribution becomes the geometric distribution.
The sum of any two negative binomial distributed variables is a negative binomial variable.
Another form of the negative binomial distribution, sometimes found in textbooks, considers only the total number of failures until the r th successful occurrence, not the total number of trials. To model this form of the distribution, subtract out r (the value of the shape parameter) from the assumption value using a formula in the worksheet.