[R] Help with hazard plots

[Alan Cox]

Hello.  I am hoping someone will be willing to help me understand something about hazard plots created with muhaz(...).  I have some background in statistics (minor in grad school), but I haven't been able to figure one thing about hazard plots.  I am using hazard plots to track customer cancellations.  I figure I can treat a cancellation as a "death", and if someone is still a customer today, they're right censored.  I know that a hazard plot shows the probability that someone will cancel in month  n  given that they're a customer in month n-1 . 


If a customer signs up on January 1st and cancels on January 2nd, we've had what I thought was an intellectual but pointless debate about whether we count that as being a customer for 1 month or 0 months.  I thought the two plots would be identical, except for a different X axis. 


However, when I create the two plots, they are very different ... very, very different.  I've posted the two plots to Flickr: 


http://flickr.com/photos/alancox/2720915878/in/photostream/ shows the plot where the lifetime of a customer who signs up on Jan 1 and cancels on Jan 2 is 0.

http://flickr.com/photos/alancox/2720915904/in/photostream/ shows the plot where the lifetime of a customer who signs up on Jan 1 and cancels on Jan 2 is 1.

My question is: Why are these two so different?  How do I know which is right?

The call that I'm making to produce the model is:

hazardV08 <- muhaz(nmc,s,max.time=max(nmc))


-- 
Alan Cox 
Director, User Experience 
iContact, Corp. 
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