# NEGBINOM.DIST function

Returns the negative binomial distribution, the probability that there will be Number_f failures before the Number_s-th success, with Probability_s probability of a success.

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. NEGBINOM.DIST calculates the probability that you will interview a certain number of unqualified candidates before finding all 10 qualified candidates.

## Syntax

`NEGBINOM.DIST(number_f,number_s,probability_s,cumulative)`

The NEGBINOM.DIST 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.
• Cumulative     Required. A logical value that determines the form of the function. If cumulative is TRUE, NEGBINOM.DIST returns the cumulative distribution function; if FALSE, it returns the probability density function.

## Remarks

• Number_f and number_s are truncated to integers.
• If any argument is nonnumeric, NEGBINOM.DIST returns the #VALUE! error value.
• If probability_s < 0 or if probability > 1, NEGBINOM.DIST returns the #NUM! error value.
• If number_f < 0 or number_s < 1, NEGBINOM.DIST 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)
=NEGBINOM.DIST(A2,A3,A4,TRUE) Cumulative negative binomial distribution for the terms above (0.313514)
=NEGBINOM.DIST(A2,A3,A4,FALSE) Probability 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