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


Aleatory uncertain discrete variable - negative binomial

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): INTEGER

Default: no negative binomial uncertain variables

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

Optional descriptors

Labels for the variables

Description

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

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

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.