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NEGBINOM.DIST Function

Excel 2010+

Summary

The NEGBINOM.DIST function calculates the negative binomial distribution, determining the probability of a specified number of failures before achieving a fixed number of successes in independent trials. This advanced statistical tool is essential for modeling scenarios where success count is fixed but failure trials vary.

Syntax

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

Parameters

Parameter	Type	Required	Description
number_f	`Number`	Yes	The number of failures (truncated to integer, must be ≥ 0)
number_s	`Number`	Yes	The required number of successes (truncated to integer, must be ≥ 1)
probability_s	`Number`	Yes	Probability of success on each trial (must be between 0 and 1)
cumulative	`Boolean`	Yes	Logical value: TRUE returns cumulative distribution, FALSE returns probability density

Using the NEGBINOM.DIST Function

NEGBINOM.DIST is used in statistical analysis to model the number of failures before achieving a predetermined number of successes. Perfect for quality control (defects before acceptable products), marketing (prospects before conversions), and reliability testing scenarios.

Common NEGBINOM.DIST Examples

Cumulative Distribution Example

=NEGBINOM.DIST(10,5,0.25,TRUE)

Probability of 10 or fewer failures before 5th success with 25% success rate (returns ~0.3135)

Probability Mass Example

=NEGBINOM.DIST(10,5,0.25,FALSE)

Exact probability of exactly 10 failures before 5th success (returns ~0.0550)

Quality Control Scenario

=NEGBINOM.DIST(15,10,0.3,FALSE)

Probability of exactly 15 defective items before finding 10 good ones (30% success rate)

Frequently Asked Questions

TRUE returns cumulative probability (≤ specified failures), FALSE returns exact probability for that number of failures.

Verify number_f ≥ 0, number_s ≥ 1, and 0 ≤ probability_s ≤ 1.

NEGBINOM.DIST fixes successes and varies failures; BINOM.DIST fixes trials and varies successes.

Common Errors and Solutions

#NUM! error

Cause: number_f < 0, number_s < 1, or probability_s outside [0,1] range

Solution: Ensure number_f ≥ 0, number_s ≥ 1, 0 ≤ probability_s ≤ 1

#VALUE! error

Cause: Non-numeric input provided

Solution: Use only numbers for number_f, number_s, probability_s; TRUE/FALSE for cumulative

Notes

Arguments number_f and number_s are truncated to integers
If cumulative=FALSE, returns probability mass function
Ideal for modeling inspection processes until quality threshold met
Replaces deprecated NEGBINOMDIST function

Compatibility

Available in: Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Excel 365

Not available in: Excel 2007, Excel 2003, Earlier versions

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2010+