Bernoulli distribution
E582379
The Bernoulli distribution is a fundamental discrete probability distribution that models a single trial with exactly two possible outcomes, typically labeled success and failure, with a fixed probability of success.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
discrete distribution
ⓘ
probability distribution ⓘ two-point distribution ⓘ |
| belongsToFamily | exponential family ⓘ |
| characteristicFunction | φ(t)=1-p+pe^{it} ⓘ |
| conjugatePrior | Beta distribution for p ⓘ |
| cumulativeDistributionFunction |
F(x)=0 for x<0
ⓘ
F(x)=1 for x≥1 ⓘ F(x)=1-p for 0≤x<1 ⓘ |
| entropy | -p log p - (1-p) log(1-p) ⓘ |
| expectedValue | p ⓘ |
| hasSupport | {0,1} ⓘ |
| isBuildingBlockOf |
binomial distribution
ⓘ
geometric distribution ⓘ negative binomial distribution ⓘ |
| isSpecialCaseOf |
Poisson binomial distribution
NERFINISHED
ⓘ
binomial distribution ⓘ categorical distribution ⓘ |
| kurtosisExcess | (1-6p(1-p))/(p(1-p)) ⓘ |
| mean | p ⓘ |
| mode |
0 and 1 if p=0.5
ⓘ
0 if p<0.5 ⓘ 1 if p>0.5 ⓘ |
| models | single trial with two outcomes ⓘ |
| momentGeneratingFunction | M(t)=1-p+pe^t ⓘ |
| namedAfter | Jacob Bernoulli NERFINISHED ⓘ |
| naturalParameter | log(p/(1-p)) ⓘ |
| parameter | p ⓘ |
| parameterDomain | 0 ≤ p ≤ 1 ⓘ |
| parameterType | probability of success ⓘ |
| probabilityGeneratingFunction | G(s)=1-p+ps ⓘ |
| probabilityMassFunction |
P(X=0)=1-p
ⓘ
P(X=1)=p ⓘ |
| randomVariableType | binary random variable ⓘ |
| skewness | (1-2p)/sqrt(p(1-p)) ⓘ |
| specialCaseParameter | binomial distribution with n=1 ⓘ |
| standardDeviation | sqrt(p(1-p)) ⓘ |
| sufficientStatistic | X ⓘ |
| supportType | discrete ⓘ |
| takesValue |
0
ⓘ
1 ⓘ |
| typicalOutcomeLabel |
failure
ⓘ
success ⓘ |
| usedIn |
A/B testing
ⓘ
binary classification modeling ⓘ coin toss modeling ⓘ logistic regression likelihood ⓘ success–failure experiments ⓘ |
| variance | p(1-p) ⓘ |
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.