Exponential model
In the last section, we studied the non-parametric Kaplan-Meier survival model. We will now bridge parametric modeling with the exponential model and then will discuss a semi-parametric model, the Cox Proportional Hazards model, in the next section. Before considering the exponential model, we will review what the exponential distribution is and why we mention it in this section. This distribution is based on the Poisson process. Here, events occur independently over time and the event rate, λ, is calculated by the number of occurrences per unit of time, as follows:
λ = Y _ t
The Poisson distribution is a statistical discrete distribution concerning the number of events occurring in a specified time period. It is defined as follows. Let Y be the number of occurrences in time t. Y follows the Poisson distribution with parameter λ if a probability mass function is given by the following formula:
f(Y) = Pr(y = Y) = e ...
