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The Excel NEGBINOM.DIST Function
Binomial and Negative Binomial Distributions
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.
The Negative Binomial Distribution is related to this function. However, for the Negative Binomial Distribution, the number of successes is fixed and the number of trials varies. The function calculates the probability of a given number of failures occurring, before the fixed number of successes is obtained. The following two forms are used:
Basic DescriptionGiven the probability of a success from a single event, the Excel NEGBINOM.DIST function calculates the probability mass function or the cumulative distribution function for the Negative Binomial Distribution. This gives the probability that there will be a given 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 Negbinom.Dist function will calculate the probability that you will toss 10 tails before you toss 12 heads. The Negbinomdist.Dist function is new in Excel 2010, and so is not available in earlier versions of Excel. However the negative binomial probability mass function can be calculated by the Negbinomdist function, which is available in earlier versions of Excel. The format of the Excel Negbinom.Dist function is:
NEGBINOM.DIST( number_f, number_s, probability_s, cumulative )
where the arguments are as follows :
Note that, if the number_f and number_s arguments are input as decimals, these values are truncated to integers. Negbinom.Dist Function Examples
Negative Binomial Distribution Function Showing the Probability
of exactly x Tails Before 12 Heads from a Tossed Coin Example 1 - Probability Mass FunctionIn the chart on the right, the Negative Binomial Probability Mass Function is used to show, for a tossed coin, the probability that exactly x tails will be tossed before the toss of a coin results in 12 tossed heads. The spreadsheets below show the Excel Negbinom.Dist function used to evaluate this function for three different values of x. The functions are displayed in the spreadsheet on the left and the results are shown in the spreadsheet on the right. Clearly, the probability of tossing a head on any one trial is 50%, so this is the value of the probability argument.
Cumulative Negative Binomial Distribution Function Showing the Probability
of at most x Tails Before 12 Heads from a Tossed Coin Example 2 - Cumulative Distribution FunctionIn the chart on the right, the Cumulative Negative Binomial Function is used to show the probability, for a tossed coin, that at most x tails will be tossed before the toss of a coin results in 12 tossed heads. The spreadsheets below show the Excel Negbinom.Dist function used to evaluate this function for three different values of x. Again, the functions are displayed in the spreadsheet on the left and the results are shown in the spreadsheet on the right.
Further examples of the Excel Negbinom.Dist function can be found on the Microsoft Office website. Trouble ShootingIf you get an error from the Excel Negbinom.Dist Function, this is likely to be one of the following: Common Errors
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