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Dakota Reference Manual
Version 6.16
Explore and Predict with Confidence
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Aleatory uncertain discrete variable - binomial
This keyword is related to the topics:
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 | ||
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.
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.