.. _variables-negative_binomial_uncertain-probability_per_trial:

"""""""""""""""""""""
probability_per_trial
"""""""""""""""""""""


A negative binomial distribution parameter



.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* prob_per_trial 

- *Arguments:* REALLIST


**Description**


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:

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

where

- :math:`p`  is the probability of success per trial
- :math:`n`  is the number of successful trials
- :math:`X`  is the number of failures



