Dakota Reference Manual: binomial_uncertain

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binomial_uncertain

Aleatory uncertain discrete variable - binomial

## Topics

This keyword is related to the topics:

- discrete_variables
- aleatory_uncertain_variables

## Specification

Alias: none

Argument(s): INTEGER

Default: no binomial uncertain variables

Child Keywords:

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

## Description

The binomial distribution describes probabilities associated with a series of independent Bernoulli trials. A Bernoulli trial is an event with two mutually exclusive outcomes, such as 0 or 1, yes or no, success or fail. The probability of success remains the same (the trials are independent).

The density function for the binomial distribution is given by:

where `p` is the probability of failure per trial, `n` is the number of trials and `x` is the number of successes.

## Theory

The binomial distribution is typically used to predict the number of failures or defective items in a total of `n` independent tests or trials, where each trial has the probability `p` of failing or being defective.