Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Aleatory uncertain discrete variable  binomial
This keyword is related to the topics:
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 
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.