Category:Definitions/Negative Binomial Distribution
Jump to navigation
Jump to search
This category contains definitions related to Negative Binomial Distribution.
Related results can be found in Category:Negative Binomial Distribution.
Let $X$ be a discrete random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
There are two forms of the negative binomial distribution, as follows:
First Form
$X$ has the negative binomial distribution (of the first form) with parameters $n$ and $p$ if:
- $\Img X = \set {0, 1, 2, \ldots}$
- $\map \Pr {X = k} = \dbinom {n + k - 1} {n - 1} p^k \paren {1 - p}^n$
where $0 < p < 1$.
It is frequently seen as:
- $\map \Pr {X = k} = \dbinom {n + k - 1} {n - 1} p^k q^n$
where $q = 1 - p$.
Second Form
$X$ has the negative binomial distribution (of the second form) with parameters $n$ and $p$ if:
- $\Img X = \set {n, n + 1, n + 2, \dotsc}$
- $\map \Pr {X = k} = \dbinom {k - 1} {n - 1} p^n \paren {1 - p}^{k - n}$
where $0 < p < 1$.
It is frequently seen as:
- $\map \Pr {X = k} = \dbinom {k - 1} {n - 1} q^{k - n} p^n $
where $q = 1 - p$.
Pages in category "Definitions/Negative Binomial Distribution"
The following 6 pages are in this category, out of 6 total.
N
- Definition:Negative Binomial Distribution
- Definition:Negative Binomial Distribution (First Form)
- Definition:Negative Binomial Distribution (Second Form)
- Definition:Negative Binomial Distribution/First Form
- Definition:Negative Binomial Distribution/Notation
- Definition:Negative Binomial Distribution/Second Form