Tukey's lambda distribution
E371258
Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Tukey's lambda distribution canonical | 1 |
| Tukey’s lambda distribution | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3600021 — 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: Tukey's lambda distribution Context triple: [John W. Tukey, developedConcept, Tukey's lambda distribution]
-
A.
Cauchy distribution
The Cauchy distribution is a continuous probability distribution with heavy tails and undefined mean and variance, often used as a classic example of pathological behavior in probability theory and statistics.
-
B.
Hotelling’s T-squared distribution
Hotelling’s T-squared distribution is a multivariate generalization of Student’s t-distribution used primarily for hypothesis testing and constructing confidence regions for mean vectors in multivariate statistics.
-
C.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
D.
F-distribution
The F-distribution is a continuous probability distribution widely used in statistics, especially for comparing variances and conducting analysis of variance (ANOVA) tests.
-
E.
Wishart
Wishart is a Scottish surname historically associated with notable figures in religion, politics, and academia.
- 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: Tukey's lambda distribution Target entity description: Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
-
A.
Cauchy distribution
The Cauchy distribution is a continuous probability distribution with heavy tails and undefined mean and variance, often used as a classic example of pathological behavior in probability theory and statistics.
-
B.
Hotelling’s T-squared distribution
Hotelling’s T-squared distribution is a multivariate generalization of Student’s t-distribution used primarily for hypothesis testing and constructing confidence regions for mean vectors in multivariate statistics.
-
C.
Gumbel
Gumbel is a surname most notably associated with American sportscaster Greg Gumbel.
-
D.
F-distribution
The F-distribution is a continuous probability distribution widely used in statistics, especially for comparing variances and conducting analysis of variance (ANOVA) tests.
-
E.
Wishart
Wishart is a Scottish surname historically associated with notable figures in religion, politics, and academia.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
continuous probability distribution
ⓘ
parametric statistical model ⓘ probability distribution ⓘ |
| approximates |
Cauchy distribution
ⓘ
logistic distribution ⓘ normal distribution ⓘ uniform distribution ⓘ |
| category | univariate distribution ⓘ |
| definedBy | quantile function ⓘ |
| family | one-parameter shape family ⓘ |
| field |
probability theory
ⓘ
statistics ⓘ |
| flexibility |
can generate heavy-tailed distributions
ⓘ
can generate leptokurtic distributions ⓘ can generate light-tailed distributions ⓘ can generate platykurtic distributions ⓘ |
| hasParameter |
location parameter
ⓘ
scale parameter ⓘ shape parameter lambda ⓘ |
| hasProperty |
closed-form quantile function
ⓘ
cumulative distribution function often lacks simple closed form ⓘ density often lacks simple closed form ⓘ |
| hasShapeParameter | lambda ⓘ |
| hasSpecialValue |
lambda = -1 corresponds approximately to Cauchy distribution
ⓘ
lambda = 0 corresponds approximately to logistic distribution ⓘ lambda = 0.14 corresponds approximately to normal distribution ⓘ lambda = 0.5 corresponds approximately to uniform distribution ⓘ |
| introducedBy |
John W. Tukey
ⓘ
surface form:
John Tukey
|
| introducedIn | 20th century ⓘ |
| kurtosis | controlled by lambda ⓘ |
| namedAfter |
John W. Tukey
ⓘ
surface form:
John Tukey
|
| quantileFunction |
Q(p) = mu + sigma * ((p^lambda - (1-p)^lambda)/lambda) for lambda ≠ 0
ⓘ
Q(p) = mu + sigma * log(p/(1-p)) for lambda = 0 ⓘ |
| relatedTo |
Box–Cox transformation
ⓘ
Johnson distributions ⓘ |
| samplingMethod | inverse transform sampling via quantile function ⓘ |
| skewness | zero for all lambda ⓘ |
| specialCaseOf | quantile-defined distributions ⓘ |
| support | real line ⓘ |
| symmetry | symmetric about location parameter ⓘ |
| usedFor |
distributional shape analysis
ⓘ
exploratory data analysis ⓘ modeling kurtosis ⓘ modeling skewness ⓘ robust statistical modeling ⓘ simulation studies ⓘ |
| usedIn |
Monte Carlo method
ⓘ
surface form:
Monte Carlo experiments
goodness-of-fit assessment ⓘ robustness studies ⓘ |
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: Tukey's lambda distribution Description of subject: Tukey's lambda distribution is a flexible family of probability distributions used primarily for exploratory data analysis and modeling diverse shapes of data, including varying degrees of skewness and kurtosis.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
John W. Tukey
this entity surface form:
Tukey’s lambda distribution