Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:organization
|
| gptkbp:application |
modeling number of successes in fixed number of independent Bernoulli trials
|
| gptkbp:assumes |
each trial has two possible outcomes
probability of success is constant trials are independent |
| gptkbp:cumulativeDistributionFunction |
sum_{i=0}^k C(n, i) * p^i * (1-p)^{n-i}
|
| gptkbp:firstDescribed |
gptkb:Ars_Conjectandi_(1713)
gptkb:Jacob_Bernoulli |
| gptkbp:hasSpecialCase |
Bernoulli distribution (when n=1)
|
| https://www.w3.org/2000/01/rdf-schema#label |
binomial distribution
|
| gptkbp:kurtosis |
(1-6p(1-p))/(n*p*(1-p))
|
| gptkbp:limitation |
Poisson distribution (as n→∞, p→0, np=λ)
|
| gptkbp:meaning |
n*p
|
| gptkbp:mode |
floor((n+1)*p)
|
| gptkbp:notation |
X ~ Bin(n, p)
|
| gptkbp:parameter |
n (number of trials)
p (probability of success) |
| gptkbp:PMF |
P(X = k) = C(n, k) * p^k * (1-p)^{n-k}
|
| gptkbp:relatedTo |
gptkb:negative_binomial_distribution
gptkb:hypergeometric_distribution |
| gptkbp:skewness |
(1-2p)/sqrt(n*p*(1-p))
|
| gptkbp:supports |
k = 0, 1, ..., n
|
| gptkbp:usedIn |
gptkb:probability_theory
statistics |
| gptkbp:variant |
n*p*(1-p)
|
| gptkbp:bfsParent |
gptkb:exponential_family
|
| gptkbp:bfsLayer |
5
|