ABSTRACT
F(x; -y, f3) = I - exp [ - ( x ~ 'Y) J . (8.1.2) In this notation. -y is the threshold parameter and f3 is the scale parameter. In
many applications the origin is at zero, that is, -y = 0, and in these cases the distribution is completely characterized by the single parameter [3. Basic characteristics of the exponential distribution are
and the hazard function is
The cumulative hazard function is
(8.1.4)
(8.1.5)
This distribution has been widely employed as a model in life-span distributions and in various reliability distributions. Since the hazard function is constant for all values of the random variable, it is a suitable model for lifetime data where used items are considered to be as good as new ones. In many applications where the Weibull, gamma, or other distribution might be a more appropriate model, the exponential is used as an approximation because of its simplicity and the ease with which calculations can be made.