# NEGBINOMDIST function

Returns the negative binomial distribution. NEGBINOMDIST returns the probability that there will be number_f failures before the number_s-th success, when the constant probability of a success is probability_s. 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. NEGBINOMDIST calculates the probability that you will interview a certain number of unqualified candidates before finding all 10 qualified candidates.

Important   This function has been replaced with one or more new functions that may provide improved accuracy and whose names better reflect their usage. Although this function is still available for backward compatibility, you should consider using the new functions from now on, because this function may not be available in future versions of Excel.

## Syntax

`NEGBINOMDIST(number_f,number_s,probability_s)`

The NEGBINOMDIST function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

• Number_f     Required. The number of failures.
• Number_s     Required. The threshold number of successes.
• Probability_s     Required. The probability of a success.

## Remarks

• Number_f and number_s are truncated to integers.
• If any argument is nonnumeric, NEGBINOMDIST returns the #VALUE! error value.
• If probability_s < 0 or if probability > 1, NEGBINOMDIST returns the #NUM! error value.
• If number_f < 0 or number_s < 1, NEGBINOMDIST 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

The example may be easier to understand if you copy it to a blank worksheet.

1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
Important: Do not select the row or column headers.

Selecting an example from Help

1. Press CTRL+C.
2. Create a blank workbook or worksheet.
3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
4. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

A B
Data Description
10 Number of failures
5 Threshold number of successes
0.25 Probability of a success
Formula Description (Result)
=NEGBINOMDIST(A2,A3,A4) Negative binomial distribution for the terms above (0.055049)

Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses