negative binomial distribution
GPTKB entity
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:organization
|
| gptkbp:alsoKnownAs |
gptkb:Pascal_distribution
gptkb:Polya_distribution |
| gptkbp:application |
modeling overdispersed count data
number of failures before r successes |
| gptkbp:category |
discrete distribution
|
| gptkbp:cumulativeDistributionFunction |
sum of PMFs up to k
|
| gptkbp:firstDescribed |
gptkb:John_Arbuthnot
|
| gptkbp:generalizes |
gptkb:geometric_distribution
|
| https://www.w3.org/2000/01/rdf-schema#label |
negative binomial distribution
|
| gptkbp:limitation |
Poisson distribution (as r→∞, p→0, with rp=λ)
|
| gptkbp:meaning |
r(1-p)/p
|
| gptkbp:mode |
floor((r-1)(1-p)/p)
|
| gptkbp:parameter |
number of successes (r)
probability of success (p) |
| gptkbp:PMF |
P(X=k) = C(k+r-1, k) * (1-p)^k * p^r
|
| gptkbp:relatedTo |
gptkb:binomial_distribution
|
| gptkbp:supports |
non-negative integers
|
| gptkbp:usedIn |
gptkb:probability_theory
statistics |
| gptkbp:variant |
r(1-p)/p^2
|
| gptkbp:bfsParent |
gptkb:beta_distribution
gptkb:binomial_distribution gptkb:Fisher's_logseries |
| gptkbp:bfsLayer |
6
|