Syntax. NEGBINOM.DIST(number_f,number_s,probability_s)
Definition. This function returns the probabilities of a negative binomial distributed random variable. NEGBINOM.DIST() calculates the probability that there will be number_f failures before the last number_s when the constant probability of a success is probability_s.
Arguments
number_f (required). The number of failures
number_s (required). The number of successes
probability_s (required). The probability of a success
Note
Number_f and number_s are truncated to integers. If one of the arguments isn’t a numeric expression, the NEGBINOM.DIST() function returns the #VALUE! error.
If probability_s is less than 0 or greater than 1, the NEGBINOM.DIST() function returns the #NUM! error.
If number_f is less than 0 or number_s is less than 1, the NEGBINOM.DIST() function returns the #NUM! error.
Background. This function is similar to the binomial distribution except that the number of successes is fixed and the number of trials is variable. This is called a negative binomial distribution. As with the binomial distribution, trials are assumed to be independent.
See Also
You will find more information about binomial distributions in the description of BINOM.DIST().
In a random experiment with independent repetitions and only two possible results (success or failure), the negative binomial distribution (or Pascal distribution) returns the probability of a fixed number of failures before the x-th success. The equation for a negative binomial distribution is
where
x equals number_f
r equals number_s
p equals probability_s
Example. You are on vacation in a foreign city and ask a passerby for directions. This question can be answered only with yes or no. This means that there is a probability of 50 percent that the answer is yes. Therefore, p is 0.5.
After you have asked a few people and nobody can tell you the way, you buy a map. Now you want to know the probability that you will find five people who know the way or how many “No, I’m sorry” responses you will get before you meet five people who do know the way. You calculate the probability with the NEGBINOM.DIST() function, as shown in Figure 12-101.
You can make the following statements from this result: Regarding number_f = 6 in Figure 12-101, the probability of you asking six people who don’t know the way before you ask five people who do know is 10.25 percent.