Failure Time Distribution |
Let be a nonnegative random variable representing the failure time of an individual from a homogeneous population. The survival distribution function (also known as the survivor function) of
is written as
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A mathematically equivalent way of specifying the distribution of is through its hazard function. The hazard function
specifies the instantaneous failure rate at
. If
is a continuous random variable,
is expressed as
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where is the probability density function of
. If
is discrete with masses at
, then survivor function is given by
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where =0 if
< 0 and
=1 otherwise. The discrete hazards are given by
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