negative_binomial_uncertain

Aleatory uncertain discrete variable - negative binomial

Topics

discrete_variables, aleatory_uncertain_variables

Specification

• Alias: None

• Arguments: INTEGER

• Default: no negative binomial uncertain variables

Child Keywords:

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

Description

The density function for the negative binomial distribution is given by:

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

where

• \(p\) is the probability of success per trial

• \(n\) is the number of successful trials

• \(x\) is the number of failures

Theory

The negative binomial distribution is typically used to predict the number of failures observed when repeating a test until a total of \(n\) successes have occurred, where each test has a probability \(p\) of success.