NEGBINOM.DIST function

This article describes the formula syntax and usage of the NEGBINOM.DIST function in Microsoft Excel.

Description

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:

• 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

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

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	0.3135141
=NEGBINOM.DIST(A2,A3,A4,FALSE)	Probability negative binomial distribution for the terms above	0.0550487