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negative binomial random variable
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(Definition)
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$X$ is a negative binomial random variable with parameters $r$ and $p$ if
$f_X(x) ={r+x-1 \choose x} p^r (1-p)^x$ , $x=\{0,1,...\}$
Parameters:
- $\star$
- $r > 0$
- $\star$
- $p \in [0,1]$
Syntax:
$X\sim NegBin(r,p)$
Notes:
- If $r \in \mathbb{N}$ , $X$ represents the number of failed Bernoulli trials before the $r$ th success. Note that if $r=1$ the variable is a geometric random variable.
- $E[X] = r \frac{1-p}{p}$
- $Var[X] = r \frac{1-p}{p^2}$
- $M_X(t) = (\frac{p}{1 - (1-p)e^t})^r$
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"negative binomial random variable" is owned by bgins. [ full author list (2) | owner history (1) ]
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| Other names: |
negative binomial distribution |
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Cross-references: geometric random variable, variable, number, represents, syntax, parameters
There are 3 references to this entry.
This is version 4 of negative binomial random variable, born on 2001-10-26, modified 2004-02-14.
Object id is 524, canonical name is NegativeBinomialRandomVariable.
Accessed 8006 times total.
Classification:
| AMS MSC: | 62E15 (Statistics :: Distribution theory :: Exact distribution theory) |
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Pending Errata and Addenda
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