# The PHREG Procedure

### 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 specifies the instantaneous failure rate at t. If T is a continuous random variable, is expressed as

where is the probability density function of T. If T is discrete with masses at , then survivor function is given by

where =0 if u < 0 and =1 otherwise. The discrete hazards are given by