binomial_uncertain

Aleatory uncertain discrete variable - binomial

Topics

discrete_variables, aleatory_uncertain_variables

Specification

  • Alias: None

  • Arguments: 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:

f(x)=(nx)px(1p)(nx),

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.