Survival function--relativized to every landmark I believe I'm having a problem with terminology. Or maybe I'm just misguided.
I'm doing a basic survival analysis with real world survival data. Death is failing to buy again within a year after the last purchase.
Suppose that the survival rate of our population drops to 54% at time 1 and then 52% at time 2 and then 50% at time 3. Now, if you survive to point 1, your likelihood of surviving to point 2 is excellent: over 96%. If you survive to point 2, similarly, your likelihood of surviving to point 3 are just over 96%. Now, it's pretty simple to extend out the survival curve using this procedure all the way to the end (suppose we have data extending out 25 points). Is there a name for this kind of a curve that I'm not aware of? It is basically like taking every point as a landmark and projecting the next point.
Thank you.

What you describe is the complement of the hazard function. For discrete-time data as you present, the hazard is the probability of an event (e.g., death) during a time period given that the individual survived to the beginning of that time period. So what you describe at each time point is 1 minus the hazard. The hazard function and its integral over time, the cumulative hazard, more readily extend than what you describe to situations where multiple events are possible, as would be the case if you were modeling purchases rather than a failure to purchase.
