# NEGBINOM.DIST

The NEGBINOM.DIST function calculates the negative binomial distribution, which models the number of failures that occur before a specified number of successes in a sequence of independent and identically distributed Bernoulli trials.

## Syntax

=NEGBINOM.DIST(`Number_F`

, `Number_S`

, `Probability_S`

, `Cumulative`

)

`Number_F` | The number of failures before the required number of successes. | ||

`Number_S` | The required number of successes. | ||

`Probability_S` | The probability of success in an individual trial. | ||

`Cumulative` | A logical value that determines the form of the function. If TRUE | it returns the cumulative distribution function; if FALSE | it returns the probability mass function. |

## About NEGBINOM.DIST

Delve into the world of probabilities with the NEGBINOM.DIST function in Excel. This handy tool allows you to explore the negative binomial distribution, a key concept in statistics that focuses on the probability of observing a certain number of failures before a specified number of successes in a series of independent trials. This distribution is particularly useful in scenarios where success or failure outcomes are binary and occur repeatedly with a fixed probability of success on each trial. By employing NEGBINOM.DIST, you can gain insights into the likelihood of encountering a specific number of failures before achieving the desired number of successes in your trials. Whether you're analyzing quality control processes, game probabilities, or other sequential events, the negative binomial distribution can offer valuable insights through its probability calculations.

## Examples

Imagine you are conducting a series of trials where the probability of success is 0.3 and you aim to achieve 5 successes. You want to determine the probability of experiencing 2 failures before reaching the 5 successes. The NEGBINOM.DIST formula would be:

=NEGBINOM.DIST(2, 5, 0.3, FALSE)

This will provide you with the probability of 2 failures before achieving 5 successes in your trials.

Suppose you are analyzing a game where the probability of winning each round is 0.2 and you need 3 wins. You are curious about the cumulative probability of encountering 1 loss before reaching the required 3 wins. The NEGBINOM.DIST formula would be:

=NEGBINOM.DIST(1, 3, 0.2, TRUE)

This will yield the cumulative distribution function, giving you the cumulative probability of 1 loss before achieving 3 wins in your game.

## Notes

When utilizing the NEGBINOM.DIST function, ensure that the values provided for the arguments align with the context of your scenario. The function assumes that the trials are independent and the probability of success remains constant throughout the trials. By adjusting the input values and understanding the nature of the negative binomial distribution, you can effectively leverage this function for probability calculations in various real-world situations.

## Questions

**What does the 'Number_F' parameter represent in the NEGBINOM.DIST function?**

The 'Number_F' parameter in NEGBINOM.DIST specifies the number of failures that are expected to occur before reaching the required number of successes in the given sequence of trials.

**How does the 'Cumulative' argument influence the NEGBINOM.DIST function's output?**

The 'Cumulative' argument in NEGBINOM.DIST determines whether the function returns the cumulative distribution function (TRUE) or the probability mass function (FALSE). If set to TRUE, the function provides the cumulative probability up to and including the specified number of failures. If set to FALSE, the function calculates the probability of the exact number of failures before the required successes.

**Can the NEGBINOM.DIST function be used to model real-world scenarios?**

Yes, the NEGBINOM.DIST function is commonly applied to model various real-world scenarios involving sequential trials with binary outcomes and a constant probability of success. It can help in predicting the likelihood of encountering a certain number of failures before achieving a specific number of successes in repetitive tasks or events.

## Related functions

BINOM.DIST

BINOM.INV

CRITBINOM

MULTINOMIAL

POISSON

HYPGEOM.DIST

WEIBULL.DIST