# NEGBINOMDIST

The NEGBINOMDIST function calculates the probability of a specified number of failures before achieving a target number of successes, based on a negative binomial distribution. This function is commonly used in statistical analysis to model scenarios where success and failure outcomes occur repeatedly until a certain number of successes is reached.

## Syntax

=NEGBINOMDIST(`Number_f`

, `Number_s`

, `Probability_s`

)

`Number_f` | The number of failures before the specified number of successes. |

`Number_s` | The target number of successes. |

`Probability_s` | The probability of success on each trial. |

## About NEGBINOMDIST

When analyzing scenarios involving repeated trials with success and failure outcomes, the NEGBINOMDIST function in Excel proves to be a valuable tool. This function is particularly useful for situations where the goal is to determine the likelihood of encountering a specified number of failures before achieving a desired number of successes, following a negative binomial distribution pattern. It aids in understanding the probability associated with the number of attempts required to reach the designated success milestone in a series of trials.

## Examples

Suppose you are conducting a series of experiments with a success probability of 0.3 per trial. You want to calculate the probability of encountering 5 failures before achieving 3 successes. The NEGBINOMDIST formula would be:

=NEGBINOMDIST(5, 3, 0.3)

This will return the probability of experiencing 5 failures before obtaining 3 successes in the given trials.

In another scenario with a success probability of 0.6 per trial, you wish to determine the likelihood of having 2 failures before reaching 4 successes. The NEGBINOMDIST formula would be:

=NEGBINOMDIST(2, 4, 0.6)

This calculation provides the probability of encountering 2 failures before attaining 4 successes in the experiment.

## Notes

Ensure the input values for Number_f, Number_s, and Probability_s are accurate representations of the scenario under analysis. The NEGBINOMDIST function assumes a negative binomial distribution, where the probability of success remains constant across all trials. It is essential to interpret the results in the context of the specific experiment being modeled.

## Questions

**What does the NEGBINOMDIST function calculate?**

The NEGBINOMDIST function calculates the probability of encountering a specified number of failures before achieving a target number of successes in a series of repeated trials following a negative binomial distribution pattern.

**In what scenarios is the NEGBINOMDIST function commonly used?**

The NEGBINOMDIST function is commonly used in statistical analysis to model situations where success and failure outcomes occur repeatedly until a specific number of successes is reached. It helps in understanding the likelihood of achieving a set number of successes after a certain number of failures.

**Can the NEGBINOMDIST function handle varying probabilities of success across trials?**

No, the NEGBINOMDIST function assumes a constant probability of success across all trials in its calculations. It operates based on this assumption to determine the probability of reaching the target number of successes after a specified number of failures.

**How can the results from the NEGBINOMDIST function be interpreted?**

The results obtained from the NEGBINOMDIST function represent the probability associated with encountering a specific number of failures before achieving the desired number of successes in a series of repeated trials. This information aids in assessing the likelihood of reaching the success milestone under consideration.