Negative binomial distribution
GPTKB entity
Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Probability distribution
|
| gptkbp:alsoKnownAs |
gptkb:Pascal_distribution
|
| gptkbp:application |
gptkb:insurance
Ecology Epidemiology Modeling overdispersed count data |
| gptkbp:category |
Discrete probability distribution
|
| gptkbp:compoundOf |
Poisson and Gamma distributions
|
| gptkbp:conjugatePriorFor |
gptkb:Poisson_distribution
|
| gptkbp:cumulativeDistributionFunction |
Sum of PMF up to k
|
| gptkbp:entropy |
Depends on r and p, no simple closed form
|
| gptkbp:firstDescribed |
gptkb:Siméon_Denis_Poisson
|
| gptkbp:generalizes |
Geometric distribution
|
| gptkbp:heldBy |
gptkb:Discrete_distribution
Compound distribution |
| https://www.w3.org/2000/01/rdf-schema#label |
Negative binomial distribution
|
| gptkbp:kurtosis |
6/p + (p^2/(r(1-p)))
|
| gptkbp:limitation |
Poisson distribution as r→∞, p→0
|
| gptkbp:meaning |
r(1-p)/p for failures parameterization
|
| gptkbp:mode |
floor((r-1)(1-p)/p) if r>1
|
| gptkbp:momentGeneratingFunction |
(p/(1-(1-p)e^t))^r
|
| gptkbp:overdispersedRelativeTo |
gptkb:Poisson_distribution
|
| gptkbp:parameter |
Failures before r-th success
Number of successes (r) Number of trials to achieve r successes Probability of success (p) |
| gptkbp:PMF |
P(X=k) = C(k+r-1, k) * (1-p)^k * p^r
|
| gptkbp:probabilityGeneratingFunction |
(p/(1-(1-p)t))^r
|
| gptkbp:relatedTo |
gptkb:Binomial_distribution
Geometric distribution Negative binomial process |
| gptkbp:skewness |
(2-p)/sqrt(r(1-p))
|
| gptkbp:sumOf |
Independent geometric distributions
|
| gptkbp:supportedBy |
k = 0, 1, 2, ...
|
| gptkbp:supports |
Non-negative integers
|
| gptkbp:usedIn |
gptkb:Probability_theory
gptkb:Bioinformatics Bayesian statistics Statistics Modeling insurance claims Actuarial science RNA-seq data analysis Count regression Generalized linear models (GLM) Modeling accident counts Modeling disease incidence Modeling ecological abundance Modeling sports statistics |
| gptkbp:variant |
r(1-p)/p^2 for failures parameterization
|
| gptkbp:bfsParent |
gptkb:Binomial_distribution
|
| gptkbp:bfsLayer |
7
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