Chapter 4 Q4.5 part 1

Hi,

In the question 4.5 of chapter 4, the part 1 is asking for generator matrix of different states. I understood that the expected waiting time has to be considered for each state while calculating the transition, but why are we considering negative signs under the same states, where no such transition is possible?

Like under state A, we have -0.5, but a claim would not be staying under state A after 2 days, so why this -0.5 under A to A? Similar values are present under other states as well.

Any help would be appreciated!

Thanks and regards,
Shyam

 

Sum of each row of a generator matrix has to be 0. So we add all the other states' transition rates and subtract the same from state A so as to make it 0. It means that that the transition rate of going out of state A is -0.5.

 

Oh yes, i get it now. I was in the concept that transition matrix's rows should be total 1, but here we are referring to generator matrix.

Thanks Srijana!

 

Welcome