Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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binomial_uncertain


Aleatory uncertain discrete variable - binomial

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): INTEGER

Default: no binomial uncertain variables

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

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:

\[f(x) = \left(\begin{array}{c}n\\x\end{array}\right){p^x}{(1-p)^{(n-x)}}\]

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.