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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Bernoulli distribution canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T6293474 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bernoulli distribution Context triple: [Bernoulli family, knownFor, Bernoulli distribution]
-
A.
Bernoulli trials
Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
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B.
Bernoulli
Bernoulli is the surname of a prominent Swiss family of mathematicians and scientists, including figures such as Jakob, Johann, and Daniel Bernoulli, who made foundational contributions to calculus, probability, and fluid dynamics.
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C.
Dirichlet distribution
The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
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D.
Poisson
Poisson is a French surname most famously associated with Siméon Denis Poisson, a prominent 19th-century mathematician and physicist known for major contributions to probability theory and mathematical physics.
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E.
Pareto distribution
The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bernoulli distribution Target entity description: 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.
-
A.
Bernoulli trials
Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
-
B.
Bernoulli
Bernoulli is the surname of a prominent Swiss family of mathematicians and scientists, including figures such as Jakob, Johann, and Daniel Bernoulli, who made foundational contributions to calculus, probability, and fluid dynamics.
-
C.
Dirichlet distribution
The Dirichlet distribution is a family of continuous multivariate probability distributions commonly used as a prior over categorical or multinomial parameters in Bayesian statistics.
-
D.
Poisson
Poisson is a French surname most famously associated with Siméon Denis Poisson, a prominent 19th-century mathematician and physicist known for major contributions to probability theory and mathematical physics.
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E.
Pareto distribution
The Pareto distribution is a power-law probability distribution often used to model phenomena with heavy tails and strong inequality, such as wealth or city sizes.
- F. None of above. chosen
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
ⓘ
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
ⓘ
linked to:
Jakob Bernoulli
|
| 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) ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Bernoulli distribution Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.