This article describes the formula syntax and usage of the NEGBINOM.DIST function in Microsoft Excel.
Description
Returns the negative binomial distribution, the probability that there will be Number_f failures before the Number_sth success, with Probability_s probability of a success.
This function is similar to the binomial distribution, except that the number of successes is fixed, and the number of trials is variable. Like the binomial, trials are assumed to be independent.
For example, you need to find 10 people with excellent reflexes, and you know the probability that a candidate has these qualifications is 0.3. NEGBINOM.DIST calculates the probability that you will interview a certain number of unqualified candidates before finding all 10 qualified candidates.
Syntax
NEGBINOM.DIST(number_f,number_s,probability_s,cumulative)
The NEGBINOM.DIST function syntax has the following arguments:

Number_f Required. The number of failures.

Number_s Required. The threshold number of successes.

Probability_s Required. The probability of a success.

Cumulative Required. A logical value that determines the form of the function. If cumulative is TRUE, NEGBINOM.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.
Remarks

Number_f and number_s are truncated to integers.

If any argument is nonnumeric, NEGBINOM.DIST returns the #VALUE! error value.

If probability_s < 0 or if probability > 1, NEGBINOM.DIST returns the #NUM! error value.

If number_f < 0 or number_s < 1, NEGBINOM.DIST returns the #NUM! error value.

The equation for the negative binomial distribution is:
where:
x is number_f, r is number_s, and p is probability_s.
Example
Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.
Data 
Description 

10 
Number of failures 

5 
Threshold number of successes 

0.25 
Probability of a success 

Formula 
Description 
Result 
=NEGBINOM.DIST(A2,A3,A4,TRUE) 
Cumulative negative binomial distribution for the terms above 
0.3135141 
=NEGBINOM.DIST(A2,A3,A4,FALSE) 
Probability negative binomial distribution for the terms above 
0.0550487 