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)
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 x1 < x2 < ... , then h(t) is given by
for j = 1, 2, ...
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