Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:inequality
|
| gptkbp:applies_to |
convex functions
concave functions |
| gptkbp:has_applications_in |
gptkb:machine_learning
information theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Jensen's Inequality
|
| gptkbp:is_a |
gptkb:theorem
inequality theorem fundamental result |
| gptkbp:is_applied_in |
risk management
random variables integrals portfolio theory finance models |
| gptkbp:is_cited_in |
gptkb:textbooks
research articles academic papers |
| gptkbp:is_debated_in |
gptkb:Mathematics
mathematical induction |
| gptkbp:is_expressed_in |
E[f(X)] ≤ f(E[ X]) for concave f
E[f(X)] ≥ f(E[ X]) for convex f |
| gptkbp:is_related_to |
gptkb:analysis
probability theory utility theory Cauchy-Schwarz inequality risk aversion expected value exponential functions logarithmic functions Minkowski inequality |
| gptkbp:is_taught_in |
economics courses
mathematics courses finance courses statistics courses |
| gptkbp:is_used_in |
economics
finance statistics risk assessment optimization problems decision theory |
| gptkbp:is_used_to |
evaluate performance
support decision making compare distributions prove other inequalities analyze variance estimate expectations derive bounds |
| gptkbp:named_after |
Johan Jensen
|
| gptkbp:state |
the value of a convex function at the mean is less than or equal to the mean of the function values
|
| gptkbp:bfsParent |
gptkb:Michael_C._Jensen
|
| gptkbp:bfsLayer |
7
|