probability_per_trial

A negative binomial distribution parameter

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:

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

where

• $p$ is the probability of success per trial

• $n$ is the number of successful trials

• $X$ is the number of failures