Chapter 10 queries

1.Why does the poisson model not allow increments?

2. Chapter 10age 17-Please explain this part:
Under the observational plan described above, the poisson model is not an exact model, since it allows a non zero probability of more than N deaths. But it is often a good approximation, since the probability of more than N deaths is usually negligible

3. Can I say that the reason why the two state model can consider the time at which a transition takes place is cause it uses mu whereas the binomial cannot as it uses a moment estimate to calculate qx?

 

(1) I'm not quite sure what you're asking here, sorry.

(2) The Poisson model says that the number of deaths is Poisson distributed. A Poisson distribution can in theory be any positive integer. Since you only have N people that can die, obviously it's impossible to actually get more than N deaths. However, if you actually look at P(deaths>N) it's clear the probability is very low.

(3) The difference is how you estimate the parameters, which comes from the likelihood functions. For binomial, you just need to know in which time interval the life died; for the two state model you need the exact time spent alive so you need the exact time of death.

 

Thank you very much.

 

Poisson model allows independent increments.