Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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A negative binomial distribution parameter


Alias: none

Argument(s): INTEGERLIST


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.

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

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


  • $p$ is the probability of success per trial
  • $n$ is the number of successful trials
  • $X$ is the number of failures