NEGBINOMDIST Function

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.

 Formulas:

Examples of use of the Excel Negbinomdist Function

 Results:

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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