2

For part of some software documentation, I created this image of the relationships between survival analysis entities: survival, CDF, PDF, hazard and cumulative hazard (see image below). There is an obvious horizontal "symmetry" in the image. Is this a consequence of some higher mathematics? Or is this a consequence of mathematicians are humans and like things to look and feel alike? Or neither, and it's just by chance.

survival analysis relationships

Cam.Davidson.Pilon
  • 436
  • 3
  • 13
  • There are a number of symmetries to be found here. Some are a result of how you organized the graph, some are the result of the concept of "inverse". Some are the result of the fact that "rate of change" is something that is almost universally applicable. Which symmetry are you referring to? – Paul Sinclair Aug 04 '19 at 14:57
  • The symmetry I am most interested in is what I call the horizontal one. On the top and bottom are two important objects related to S(t) by an invertible function, and differentiating gives another function of importance (hazard and pdf). From a different perspective: the operations done in "hazard" space are identical to the operations done in "probability" space. Is this interesting? – Cam.Davidson.Pilon Aug 04 '19 at 16:58

0 Answers0