## Failure Time Distribution

Let *T* 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 *T* is written as

A mathematically equivalent way of specifying the distribution
of *T* is through its hazard function. The hazard function *h*(*t*)
specifies
the instantaneous failure rate at *t*. If *T* is a continuous random variable,
*h*(*t*) is expressed as

where *f*(*t*) is the probability density function of *T*. If *T* is discrete
with masses at *x*_{1} < *x*_{2} < ... , then *h*(*t*) is given by

where

for *j* = 1, 2, ...

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