Formulas and functions > Functions from A to Z > NEGBINOM.DIST (negative binomial distribution)

Syntax:

NEGBINOM.DIST(k, r, p, Cumulative)

Description:

This returns the negative binomial distribution (also known as Pascal distribution).

The negative binomial distribution can be used to calculate the probability of obtaining k failures before the r-th success in a random experiment with independent trials and only two possible outcomes (success or failure) with a fixed probability of p for each trial.

k is the number of failures. It must be ≥ 0.

r is the number of successes. It must be ≥ 0.

k and r should be integers. If this is not the case, PlanMaker automatically truncates the decimal places.

p is the probability of success for each trial run. It must be within the range 0 to 1.

Cumulative determines the type of function as a switch: If you enter the value TRUE, the cumulative distribution function of the negative binomial distribution is calculated. By entering the value FALSE, the probability density function of the negative binomial distribution is calculated.

Example:

An urn contains 1 red ball and 5 black balls. What is the probability (with the balls being returned) of drawing exactly or at most 10 black balls (failures) before the 2nd red ball (success) is drawn?

NEGBINOM.DIST(10, 2, 1/6, FALSE) returns 0.04935

NEGBINOM.DIST(10, 2, 1/6, TRUE) returns 0.61867

The probability of having to draw exactly 10 black balls is 4.9% (probability density function). The probability of having to draw at most 10 black balls is 61.9% (cumulative distribution function).

Note:

The NEGBINOM.DIST function supplements the previous NEGBINOMDIST function with the additional argument Cumulative.

Compatibility notes:

Microsoft Excel supports this function only in version 2010 or later. The function is unknown in older versions.