Basic Description

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 the probability of 50%, that the toss of a coin will land on heads, the Negbinomdist function will calculate the probability that you will toss 10 tails before you toss 12 heads.

Syntax: NEGBINOMDIST( number_f, number_s, probability_s )

where the arguments are listed in the table below :

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 the values input for the number_f and number_s arguments are decimal numbers, they are truncated to integers by Excel.

Binomial Distribution Probability Mass Function Chart

Negative Binomial Distribution Function Showing the Probability
of x Tails Before 12 Heads from a Tossed Coin

Negbinomdist Function Examples

The chart on the right shows the Negative Binomial Distribution Function for the probability that x tails will be tossed before the toss of a coin results in 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 50%, so this is input as the probability argument to the functions.


Examples of use of the Excel Negbinomdist Function


Excel Negbinomdist Function Results


Negbinomdist Function Errors

If you get an error from the Excel Negbinomdist Function, this is likely to be one of the following:

#NUM! Occurs if either the supplied number_f is < 0 or the supplied number_s is < 1 or the supplied probability_s is < 0 or > 1
#VALUE! Occurs if any of the number_f, number_s, or probability_s arguments are nonnumeric

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