Dakota Reference Manual: negative_binomial_uncertain

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negative_binomial_uncertain

Aleatory uncertain discrete variable - negative binomial

## Topics

This keyword is related to the topics:

- discrete_variables
- aleatory_uncertain_variables

## Specification

Alias: none

Argument(s): INTEGER

Default: no negative binomial uncertain variables

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required | probability_per_trial | A negative binomial distribution parameter
| Required | num_trials | A negative binomial distribution parameter
| Optional | initial_point | Initial values for variables
| Optional | descriptors | Labels for the variables

## Description

The density function for the negative binomial distribution is given by:

where

- is the probability of success per trial
- is the number of successful trials
- is the number of failures

## Theory

The negative binomial distribution is typically used to predict the number of failures observed when repeating a test until a total of `n` successes have occurred, where each test has a probability `p` of success.