Category:Survival Functions

This category contains results about Survival Functions.
Definitions specific to this category can be found in Definitions/Survival Functions.

Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let $f: X \to \overline \R$ be a $\Sigma$-measurable function.

The survival function of $f$ is the mapping $F_f: \R \to \overline \R$ defined by:

$\forall t \in \R: \map {F_f} t := \map \mu {\set {\size f \ge t} }$

where $\set {\size f \ge t}$ denotes the set $\set {x \in X: \size {\map f x} \ge t}$.