Dear All, I am unable to understand the significance of age-dependent "Transition Intensity". Please refer Section 1 of Chapter 4 {The two-state Markov model} in CT4 Acted Study Material the following is written. tqx = P [person in dead state at age 'x+t' | in alive state at age 'x' ] I can't understand the Transition intensity µx+t given in limiting form. Can anyone kindly write the physical significance of the mathematical form of it while dt → 0. Thanks in advance ! Sumon
tqx can be thought of as a binomial probability. The probability of faliure (or sucess if you like). Ie. the probability of death between the ages of x and x+t given alive at age x. µx+t can be expressed in a number of different ways. It is the instantaneous rate of mortality. Ie. lim (dt->0) [dtqx+t]/dt. Consider q_x+t as a function of time, This is like the definition of a derivative lim dt->0[f(x+dt)-f(x)]/dt, except in this case the consideration is lim dt->0 [dt_q_x+t - 0_q_x+t]/dt. Ie. the interest is in the change in the function q_x+t over an infinitesimally small time period [the numerator] divided by the length of that time period. The physical significance being that the probability of death over a very small time interval dt is approximately the length of that interval multiplied by the force of mortality at that instant mu_x+t (plus some small error term).
Hi DevonMatthews, THANK YOU VERY MUCH FOR YOUR CLARIFICATION. I HAVE UNDERSTOOD CLEARLY THE IDEA OF IT.THANKS A LOT.
