characteristic function (probability theory)
GPTKB entity
Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alternativeTo |
moment generating function
|
| gptkbp:appliesTo |
probability measure
random variable |
| gptkbp:author |
gptkb:Paul_Lévy
|
| gptkbp:category |
mathematical analysis
probability distributions |
| gptkbp:codomain |
complex numbers
|
| gptkbp:defines |
E[e^{itX}]
|
| gptkbp:describes |
gptkb:organization
|
| gptkbp:domain |
real numbers
|
| gptkbp:field |
gptkb:probability_theory
statistics |
| gptkbp:heldBy |
Fourier transform of probability density function
|
| https://www.w3.org/2000/01/rdf-schema#label |
characteristic function (probability theory)
|
| gptkbp:inverse_transform |
inversion formula
|
| gptkbp:notation |
φ_X(t)
|
| gptkbp:property |
continuous
always exists uniquely determines distribution |φ_X(t)| ≤ 1 φ_X(0) = 1 |
| gptkbp:relatedConcept |
gptkb:Laplace_transform
cumulant generating function |
| gptkbp:usedFor |
finding moments
proving limit theorems studying distribution properties |
| gptkbp:bfsParent |
gptkb:Bochner's_theorem
|
| gptkbp:bfsLayer |
6
|