The Binomial Distribution is a statistical measure that is frequently used to indicate the probability of a specific number of successes occurring from a specific number of independent trials.
For the Negative Binomial Distribution, the number of successes is fixed and the number of trials varies. The function calculates the probability of a specific number of failures occurring, before the fixed number of successes is obtained.
Further information can be found on the Wikipedia Negative Binomial Distribution pageIn Excel 2010, the Negbinomdist function has been replaced by the Negbinom.Dist function, which has improved accuracy.
Although it has been replaced, the Negbinomdist function is still available in Excel 2010 (stored in the list of compatibility functions), to allow compatibility with earlier versions of Excel.
However, the Negbinomdist function may not be available in future versions of Excel, so it is advised that you use the Negbinom.Dist function if possible.
Given the probability of a success from a single event, the Excel NEGBINOMDIST function calculates the Negative Binomial Distribution for a given set of parameters.
This gives the probability that there will be a specified number of failures before a required number of successes is achieved.
For example, given the probability of 50%, that the toss of a coin will land on heads, the Negbinomdist function can be used to calculate the probability that you will toss 10 tails before you toss 12 heads.
The syntax of the function is:
where the arguments are as follows:
number_f    The number of failures encountered before number_s successes. 
number_s    The required number of successes. 
probability_s    The probability of success in one trial. 
Note that, if decimal values are entered for the number_f and number_s arguments, these are truncated to integers by Excel.
The above chart on the right shows the Negative Binomial Distribution Function for the probability that the toss of a coin will result in exactly x tails before 12 tossed heads.
The spreadsheets below show the Excel Negbinomdist function used to evaluate this function for three different values of x.
Clearly, the probability of tossing a head on any one trial is 0.5, so this is input as the probability argument to the functions.
Formulas:

Results:

For further examples of the Excel Negbinomdist function, see the Microsoft Office website.
If you get an error from the Excel Negbinomdist Function, this is likely to be one of the following:
#NUM!   
Occurs if either:

#VALUE!    Occurs if any of the number_f, number_s, or probability_s arguments are nonnumeric. 