Survival function

The survival function gives the probability that a random variable exceeds a value x, which is one minus its cumulative distribution function. It is widely used in reliability engineering and survival analysis to model the time until an event occurs.

F ˉ_{X} (x) = P (X > x) = 1 - F_{X} (x)

\bar{F}_{X}(x) = \mathrm{P}(X > x) = 1 - F_{X}(x)

What the symbols mean

$X$	random variable, often a time to an event
$x$	value at which the function is evaluated
$F ˉ_{X} (x)$	survival function of X at x
$F_{X} (x)$	cumulative distribution function of X at x
$P (X > x)$	probability that X exceeds x

About this formula

FieldStatistics
TopicProbability distributions
LevelUniversity
Also calledsurvivor function, reliability function, complementary CDF, CCDF, tail distribution function, exceedance
SourceWikidata Q2915096

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